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!function(e){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=e();else if("function"==typeof define&&define.amd)define([],e);else{var f;"undefined"!=typeof window?f=window:"undefined"!=typeof global?f=global:"undefined"!=typeof self&&(f=self),f.dagre=e()}}(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o 0; --i) {
entry = buckets[i].dequeue();
if (entry) {
results = results.concat(removeNode(g, buckets, zeroIdx, entry, true));
break;
}
}
}
}
return results;
}
function removeNode(g, buckets, zeroIdx, entry, collectPredecessors) {
var results = collectPredecessors ? [] : undefined;
_.each(g.inEdges(entry.v), function(edge) {
var weight = g.edge(edge),
uEntry = g.node(edge.v);
if (collectPredecessors) {
results.push({ v: edge.v, w: edge.w });
}
uEntry.out -= weight;
assignBucket(buckets, zeroIdx, uEntry);
});
_.each(g.outEdges(entry.v), function(edge) {
var weight = g.edge(edge),
w = edge.w,
wEntry = g.node(w);
wEntry["in"] -= weight;
assignBucket(buckets, zeroIdx, wEntry);
});
g.removeNode(entry.v);
return results;
}
function buildState(g, weightFn) {
var fasGraph = new Graph(),
maxIn = 0,
maxOut = 0;
_.each(g.nodes(), function(v) {
fasGraph.setNode(v, { v: v, "in": 0, out: 0 });
});
// Aggregate weights on nodes, but also sum the weights across multi-edges
// into a single edge for the fasGraph.
_.each(g.edges(), function(e) {
var prevWeight = fasGraph.edge(e.v, e.w) || 0,
weight = weightFn(e),
edgeWeight = prevWeight + weight;
fasGraph.setEdge(e.v, e.w, edgeWeight);
maxOut = Math.max(maxOut, fasGraph.node(e.v).out += weight);
maxIn = Math.max(maxIn, fasGraph.node(e.w)["in"] += weight);
});
var buckets = _.range(maxOut + maxIn + 3).map(function() { return new List(); });
var zeroIdx = maxIn + 1;
_.each(fasGraph.nodes(), function(v) {
assignBucket(buckets, zeroIdx, fasGraph.node(v));
});
return { graph: fasGraph, buckets: buckets, zeroIdx: zeroIdx };
}
function assignBucket(buckets, zeroIdx, entry) {
if (!entry.out) {
buckets[0].enqueue(entry);
} else if (!entry["in"]) {
buckets[buckets.length - 1].enqueue(entry);
} else {
buckets[entry.out - entry["in"] + zeroIdx].enqueue(entry);
}
}
},{"./data/list":5,"./graphlib":7,"./lodash":10}],9:[function(require,module,exports){
"use strict";
var _ = require("./lodash"),
acyclic = require("./acyclic"),
normalize = require("./normalize"),
rank = require("./rank"),
normalizeRanks = require("./util").normalizeRanks,
parentDummyChains = require("./parent-dummy-chains"),
removeEmptyRanks = require("./util").removeEmptyRanks,
nestingGraph = require("./nesting-graph"),
addBorderSegments = require("./add-border-segments"),
coordinateSystem = require("./coordinate-system"),
order = require("./order"),
position = require("./position"),
util = require("./util"),
Graph = require("./graphlib").Graph;
module.exports = layout;
function layout(g, opts) {
var time = opts && opts.debugTiming ? util.time : util.notime;
time("layout", function() {
var layoutGraph = time(" buildLayoutGraph",
function() { return buildLayoutGraph(g); });
time(" runLayout", function() { runLayout(layoutGraph, time); });
time(" updateInputGraph", function() { updateInputGraph(g, layoutGraph); });
});
}
function runLayout(g, time) {
time(" makeSpaceForEdgeLabels", function() { makeSpaceForEdgeLabels(g); });
time(" removeSelfEdges", function() { removeSelfEdges(g); });
time(" acyclic", function() { acyclic.run(g); });
time(" nestingGraph.run", function() { nestingGraph.run(g); });
time(" rank", function() { rank(util.asNonCompoundGraph(g)); });
time(" injectEdgeLabelProxies", function() { injectEdgeLabelProxies(g); });
time(" removeEmptyRanks", function() { removeEmptyRanks(g); });
time(" nestingGraph.cleanup", function() { nestingGraph.cleanup(g); });
time(" normalizeRanks", function() { normalizeRanks(g); });
time(" assignRankMinMax", function() { assignRankMinMax(g); });
time(" removeEdgeLabelProxies", function() { removeEdgeLabelProxies(g); });
time(" normalize.run", function() { normalize.run(g); });
time(" parentDummyChains", function() { parentDummyChains(g); });
time(" addBorderSegments", function() { addBorderSegments(g); });
time(" order", function() { order(g); });
time(" insertSelfEdges", function() { insertSelfEdges(g); });
time(" adjustCoordinateSystem", function() { coordinateSystem.adjust(g); });
time(" position", function() { position(g); });
time(" positionSelfEdges", function() { positionSelfEdges(g); });
time(" removeBorderNodes", function() { removeBorderNodes(g); });
time(" normalize.undo", function() { normalize.undo(g); });
time(" fixupEdgeLabelCoords", function() { fixupEdgeLabelCoords(g); });
time(" undoCoordinateSystem", function() { coordinateSystem.undo(g); });
time(" translateGraph", function() { translateGraph(g); });
time(" assignNodeIntersects", function() { assignNodeIntersects(g); });
time(" reversePoints", function() { reversePointsForReversedEdges(g); });
time(" acyclic.undo", function() { acyclic.undo(g); });
}
/*
* Copies final layout information from the layout graph back to the input
* graph. This process only copies whitelisted attributes from the layout graph
* to the input graph, so it serves as a good place to determine what
* attributes can influence layout.
*/
function updateInputGraph(inputGraph, layoutGraph) {
_.each(inputGraph.nodes(), function(v) {
var inputLabel = inputGraph.node(v),
layoutLabel = layoutGraph.node(v);
if (inputLabel) {
inputLabel.x = layoutLabel.x;
inputLabel.y = layoutLabel.y;
if (layoutGraph.children(v).length) {
inputLabel.width = layoutLabel.width;
inputLabel.height = layoutLabel.height;
}
}
});
_.each(inputGraph.edges(), function(e) {
var inputLabel = inputGraph.edge(e),
layoutLabel = layoutGraph.edge(e);
inputLabel.points = layoutLabel.points;
if (_.has(layoutLabel, "x")) {
inputLabel.x = layoutLabel.x;
inputLabel.y = layoutLabel.y;
}
});
inputGraph.graph().width = layoutGraph.graph().width;
inputGraph.graph().height = layoutGraph.graph().height;
}
var graphNumAttrs = ["nodesep", "edgesep", "ranksep", "marginx", "marginy"],
graphDefaults = { ranksep: 50, edgesep: 20, nodesep: 50, rankdir: "tb" },
graphAttrs = ["acyclicer", "ranker", "rankdir", "align"],
nodeNumAttrs = ["width", "height"],
nodeDefaults = { width: 0, height: 0 },
edgeNumAttrs = ["minlen", "weight", "width", "height", "labeloffset"],
edgeDefaults = {
minlen: 1, weight: 1, width: 0, height: 0,
labeloffset: 10, labelpos: "r"
},
edgeAttrs = ["labelpos"];
/*
* Constructs a new graph from the input graph, which can be used for layout.
* This process copies only whitelisted attributes from the input graph to the
* layout graph. Thus this function serves as a good place to determine what
* attributes can influence layout.
*/
function buildLayoutGraph(inputGraph) {
var g = new Graph({ multigraph: true, compound: true }),
graph = canonicalize(inputGraph.graph());
g.setGraph(_.merge({},
graphDefaults,
selectNumberAttrs(graph, graphNumAttrs),
_.pick(graph, graphAttrs)));
_.each(inputGraph.nodes(), function(v) {
var node = canonicalize(inputGraph.node(v));
g.setNode(v, _.defaults(selectNumberAttrs(node, nodeNumAttrs), nodeDefaults));
g.setParent(v, inputGraph.parent(v));
});
_.each(inputGraph.edges(), function(e) {
var edge = canonicalize(inputGraph.edge(e));
g.setEdge(e, _.merge({},
edgeDefaults,
selectNumberAttrs(edge, edgeNumAttrs),
_.pick(edge, edgeAttrs)));
});
return g;
}
/*
* This idea comes from the Gansner paper: to account for edge labels in our
* layout we split each rank in half by doubling minlen and halving ranksep.
* Then we can place labels at these mid-points between nodes.
*
* We also add some minimal padding to the width to push the label for the edge
* away from the edge itself a bit.
*/
function makeSpaceForEdgeLabels(g) {
var graph = g.graph();
graph.ranksep /= 2;
_.each(g.edges(), function(e) {
var edge = g.edge(e);
edge.minlen *= 2;
if (edge.labelpos.toLowerCase() !== "c") {
if (graph.rankdir === "TB" || graph.rankdir === "BT") {
edge.width += edge.labeloffset;
} else {
edge.height += edge.labeloffset;
}
}
});
}
/*
* Creates temporary dummy nodes that capture the rank in which each edge's
* label is going to, if it has one of non-zero width and height. We do this
* so that we can safely remove empty ranks while preserving balance for the
* label's position.
*/
function injectEdgeLabelProxies(g) {
_.each(g.edges(), function(e) {
var edge = g.edge(e);
if (edge.width && edge.height) {
var v = g.node(e.v),
w = g.node(e.w),
label = { rank: (w.rank - v.rank) / 2 + v.rank, e: e };
util.addDummyNode(g, "edge-proxy", label, "_ep");
}
});
}
function assignRankMinMax(g) {
var maxRank = 0;
_.each(g.nodes(), function(v) {
var node = g.node(v);
if (node.borderTop) {
node.minRank = g.node(node.borderTop).rank;
node.maxRank = g.node(node.borderBottom).rank;
maxRank = _.max(maxRank, node.maxRank);
}
});
g.graph().maxRank = maxRank;
}
function removeEdgeLabelProxies(g) {
_.each(g.nodes(), function(v) {
var node = g.node(v);
if (node.dummy === "edge-proxy") {
g.edge(node.e).labelRank = node.rank;
g.removeNode(v);
}
});
}
function translateGraph(g) {
var minX = Number.POSITIVE_INFINITY,
maxX = 0,
minY = Number.POSITIVE_INFINITY,
maxY = 0,
graphLabel = g.graph(),
marginX = graphLabel.marginx || 0,
marginY = graphLabel.marginy || 0;
function getExtremes(attrs) {
var x = attrs.x,
y = attrs.y,
w = attrs.width,
h = attrs.height;
minX = Math.min(minX, x - w / 2);
maxX = Math.max(maxX, x + w / 2);
minY = Math.min(minY, y - h / 2);
maxY = Math.max(maxY, y + h / 2);
}
_.each(g.nodes(), function(v) { getExtremes(g.node(v)); });
_.each(g.edges(), function(e) {
var edge = g.edge(e);
if (_.has(edge, "x")) {
getExtremes(edge);
}
});
minX -= marginX;
minY -= marginY;
_.each(g.nodes(), function(v) {
var node = g.node(v);
node.x -= minX;
node.y -= minY;
});
_.each(g.edges(), function(e) {
var edge = g.edge(e);
_.each(edge.points, function(p) {
p.x -= minX;
p.y -= minY;
});
if (_.has(edge, "x")) { edge.x -= minX; }
if (_.has(edge, "y")) { edge.y -= minY; }
});
graphLabel.width = maxX - minX + marginX;
graphLabel.height = maxY - minY + marginY;
}
function assignNodeIntersects(g) {
_.each(g.edges(), function(e) {
var edge = g.edge(e),
nodeV = g.node(e.v),
nodeW = g.node(e.w),
p1, p2;
if (!edge.points) {
edge.points = [];
p1 = nodeW;
p2 = nodeV;
} else {
p1 = edge.points[0];
p2 = edge.points[edge.points.length - 1];
}
edge.points.unshift(util.intersectRect(nodeV, p1));
edge.points.push(util.intersectRect(nodeW, p2));
});
}
function fixupEdgeLabelCoords(g) {
_.each(g.edges(), function(e) {
var edge = g.edge(e);
if (_.has(edge, "x")) {
if (edge.labelpos === "l" || edge.labelpos === "r") {
edge.width -= edge.labeloffset;
}
switch (edge.labelpos) {
case "l": edge.x -= edge.width / 2 + edge.labeloffset; break;
case "r": edge.x += edge.width / 2 + edge.labeloffset; break;
}
}
});
}
function reversePointsForReversedEdges(g) {
_.each(g.edges(), function(e) {
var edge = g.edge(e);
if (edge.reversed) {
edge.points.reverse();
}
});
}
function removeBorderNodes(g) {
_.each(g.nodes(), function(v) {
if (g.children(v).length) {
var node = g.node(v),
t = g.node(node.borderTop),
b = g.node(node.borderBottom),
l = g.node(_.last(node.borderLeft)),
r = g.node(_.last(node.borderRight));
node.width = Math.abs(r.x - l.x);
node.height = Math.abs(b.y - t.y);
node.x = l.x + node.width / 2;
node.y = t.y + node.height / 2;
}
});
_.each(g.nodes(), function(v) {
if (g.node(v).dummy === "border") {
g.removeNode(v);
}
});
}
function removeSelfEdges(g) {
_.each(g.edges(), function(e) {
if (e.v === e.w) {
var node = g.node(e.v);
if (!node.selfEdges) {
node.selfEdges = [];
}
node.selfEdges.push({ e: e, label: g.edge(e) });
g.removeEdge(e);
}
});
}
function insertSelfEdges(g) {
var layers = util.buildLayerMatrix(g);
_.each(layers, function(layer) {
var orderShift = 0;
_.each(layer, function(v, i) {
var node = g.node(v);
node.order = i + orderShift;
_.each(node.selfEdges, function(selfEdge) {
util.addDummyNode(g, "selfedge", {
width: selfEdge.label.width,
height: selfEdge.label.height,
rank: node.rank,
order: i + (++orderShift),
e: selfEdge.e,
label: selfEdge.label
}, "_se");
});
delete node.selfEdges;
});
});
}
function positionSelfEdges(g) {
_.each(g.nodes(), function(v) {
var node = g.node(v);
if (node.dummy === "selfedge") {
var selfNode = g.node(node.e.v),
x = selfNode.x + selfNode.width / 2,
y = selfNode.y,
dx = node.x - x,
dy = selfNode.height / 2;
g.setEdge(node.e, node.label);
g.removeNode(v);
node.label.points = [
{ x: x + 2 * dx / 3, y: y - dy },
{ x: x + 5 * dx / 6, y: y - dy },
{ x: x + dx , y: y },
{ x: x + 5 * dx / 6, y: y + dy },
{ x: x + 2 * dx / 3, y: y + dy },
];
node.label.x = node.x;
node.label.y = node.y;
}
});
}
function selectNumberAttrs(obj, attrs) {
return _.mapValues(_.pick(obj, attrs), Number);
}
function canonicalize(attrs) {
var newAttrs = {};
_.each(attrs, function(v, k) {
newAttrs[k.toLowerCase()] = v;
});
return newAttrs;
}
},{"./acyclic":2,"./add-border-segments":3,"./coordinate-system":4,"./graphlib":7,"./lodash":10,"./nesting-graph":11,"./normalize":12,"./order":17,"./parent-dummy-chains":22,"./position":24,"./rank":26,"./util":29}],10:[function(require,module,exports){
/* global window */
var lodash;
if (typeof require === "function") {
try {
lodash = require("lodash");
} catch (e) {}
}
if (!lodash) {
lodash = window._;
}
module.exports = lodash;
},{"lodash":undefined}],11:[function(require,module,exports){
var _ = require("./lodash"),
util = require("./util");
module.exports = {
run: run,
cleanup: cleanup
};
/*
* A nesting graph creates dummy nodes for the tops and bottoms of subgraphs,
* adds appropriate edges to ensure that all cluster nodes are placed between
* these boundries, and ensures that the graph is connected.
*
* In addition we ensure, through the use of the minlen property, that nodes
* and subgraph border nodes to not end up on the same rank.
*
* Preconditions:
*
* 1. Input graph is a DAG
* 2. Nodes in the input graph has a minlen attribute
*
* Postconditions:
*
* 1. Input graph is connected.
* 2. Dummy nodes are added for the tops and bottoms of subgraphs.
* 3. The minlen attribute for nodes is adjusted to ensure nodes do not
* get placed on the same rank as subgraph border nodes.
*
* The nesting graph idea comes from Sander, "Layout of Compound Directed
* Graphs."
*/
function run(g) {
var root = util.addDummyNode(g, "root", {}, "_root"),
depths = treeDepths(g),
height = _.max(depths) - 1,
nodeSep = 2 * height + 1;
g.graph().nestingRoot = root;
// Multiply minlen by nodeSep to align nodes on non-border ranks.
_.each(g.edges(), function(e) { g.edge(e).minlen *= nodeSep; });
// Calculate a weight that is sufficient to keep subgraphs vertically compact
var weight = sumWeights(g) + 1;
// Create border nodes and link them up
_.each(g.children(), function(child) {
dfs(g, root, nodeSep, weight, height, depths, child);
});
// Save the multiplier for node layers for later removal of empty border
// layers.
g.graph().nodeRankFactor = nodeSep;
}
function dfs(g, root, nodeSep, weight, height, depths, v) {
var children = g.children(v);
if (!children.length) {
if (v !== root) {
g.setEdge(root, v, { weight: 0, minlen: nodeSep });
}
return;
}
var top = util.addBorderNode(g, "_bt"),
bottom = util.addBorderNode(g, "_bb"),
label = g.node(v);
g.setParent(top, v);
label.borderTop = top;
g.setParent(bottom, v);
label.borderBottom = bottom;
_.each(children, function(child) {
dfs(g, root, nodeSep, weight, height, depths, child);
var childNode = g.node(child),
childTop = childNode.borderTop ? childNode.borderTop : child,
childBottom = childNode.borderBottom ? childNode.borderBottom : child,
thisWeight = childNode.borderTop ? weight : 2 * weight,
minlen = childTop !== childBottom ? 1 : height - depths[v] + 1;
g.setEdge(top, childTop, {
weight: thisWeight,
minlen: minlen,
nestingEdge: true
});
g.setEdge(childBottom, bottom, {
weight: thisWeight,
minlen: minlen,
nestingEdge: true
});
});
if (!g.parent(v)) {
g.setEdge(root, top, { weight: 0, minlen: height + depths[v] });
}
}
function treeDepths(g) {
var depths = {};
function dfs(v, depth) {
var children = g.children(v);
if (children && children.length) {
_.each(children, function(child) {
dfs(child, depth + 1);
});
}
depths[v] = depth;
}
_.each(g.children(), function(v) { dfs(v, 1); });
return depths;
}
function sumWeights(g) {
return _.reduce(g.edges(), function(acc, e) {
return acc + g.edge(e).weight;
}, 0);
}
function cleanup(g) {
var graphLabel = g.graph();
g.removeNode(graphLabel.nestingRoot);
delete graphLabel.nestingRoot;
_.each(g.edges(), function(e) {
var edge = g.edge(e);
if (edge.nestingEdge) {
g.removeEdge(e);
}
});
}
},{"./lodash":10,"./util":29}],12:[function(require,module,exports){
"use strict";
var _ = require("./lodash"),
util = require("./util");
module.exports = {
run: run,
undo: undo
};
/*
* Breaks any long edges in the graph into short segments that span 1 layer
* each. This operation is undoable with the denormalize function.
*
* Pre-conditions:
*
* 1. The input graph is a DAG.
* 2. Each node in the graph has a "rank" property.
*
* Post-condition:
*
* 1. All edges in the graph have a length of 1.
* 2. Dummy nodes are added where edges have been split into segments.
* 3. The graph is augmented with a "dummyChains" attribute which contains
* the first dummy in each chain of dummy nodes produced.
*/
function run(g) {
g.graph().dummyChains = [];
_.each(g.edges(), function(edge) { normalizeEdge(g, edge); });
}
function normalizeEdge(g, e) {
var v = e.v,
vRank = g.node(v).rank,
w = e.w,
wRank = g.node(w).rank,
name = e.name,
edgeLabel = g.edge(e),
labelRank = edgeLabel.labelRank;
if (wRank === vRank + 1) return;
g.removeEdge(e);
var dummy, attrs, i;
for (i = 0, ++vRank; vRank < wRank; ++i, ++vRank) {
edgeLabel.points = [];
attrs = {
width: 0, height: 0,
edgeLabel: edgeLabel, edgeObj: e,
rank: vRank
};
dummy = util.addDummyNode(g, "edge", attrs, "_d");
if (vRank === labelRank) {
attrs.width = edgeLabel.width;
attrs.height = edgeLabel.height;
attrs.dummy = "edge-label";
attrs.labelpos = edgeLabel.labelpos;
}
g.setEdge(v, dummy, { weight: edgeLabel.weight }, name);
if (i === 0) {
g.graph().dummyChains.push(dummy);
}
v = dummy;
}
g.setEdge(v, w, { weight: edgeLabel.weight }, name);
}
function undo(g) {
_.each(g.graph().dummyChains, function(v) {
var node = g.node(v),
origLabel = node.edgeLabel,
w;
g.setEdge(node.edgeObj, origLabel);
while (node.dummy) {
w = g.successors(v)[0];
g.removeNode(v);
origLabel.points.push({ x: node.x, y: node.y });
if (node.dummy === "edge-label") {
origLabel.x = node.x;
origLabel.y = node.y;
origLabel.width = node.width;
origLabel.height = node.height;
}
v = w;
node = g.node(v);
}
});
}
},{"./lodash":10,"./util":29}],13:[function(require,module,exports){
var _ = require("../lodash");
module.exports = addSubgraphConstraints;
function addSubgraphConstraints(g, cg, vs) {
var prev = {},
rootPrev;
_.each(vs, function(v) {
var child = g.parent(v),
parent,
prevChild;
while (child) {
parent = g.parent(child);
if (parent) {
prevChild = prev[parent];
prev[parent] = child;
} else {
prevChild = rootPrev;
rootPrev = child;
}
if (prevChild && prevChild !== child) {
cg.setEdge(prevChild, child);
return;
}
child = parent;
}
});
/*
function dfs(v) {
var children = v ? g.children(v) : g.children();
if (children.length) {
var min = Number.POSITIVE_INFINITY,
subgraphs = [];
_.each(children, function(child) {
var childMin = dfs(child);
if (g.children(child).length) {
subgraphs.push({ v: child, order: childMin });
}
min = Math.min(min, childMin);
});
_.reduce(_.sortBy(subgraphs, "order"), function(prev, curr) {
cg.setEdge(prev.v, curr.v);
return curr;
});
return min;
}
return g.node(v).order;
}
dfs(undefined);
*/
}
},{"../lodash":10}],14:[function(require,module,exports){
var _ = require("../lodash");
module.exports = barycenter;
function barycenter(g, movable) {
return _.map(movable, function(v) {
var inV = g.inEdges(v);
if (!inV.length) {
return { v: v };
} else {
var result = _.reduce(inV, function(acc, e) {
var edge = g.edge(e),
nodeU = g.node(e.v);
return {
sum: acc.sum + (edge.weight * nodeU.order),
weight: acc.weight + edge.weight
};
}, { sum: 0, weight: 0 });
return {
v: v,
barycenter: result.sum / result.weight,
weight: result.weight
};
}
});
}
},{"../lodash":10}],15:[function(require,module,exports){
var _ = require("../lodash"),
Graph = require("../graphlib").Graph;
module.exports = buildLayerGraph;
/*
* Constructs a graph that can be used to sort a layer of nodes. The graph will
* contain all base and subgraph nodes from the request layer in their original
* hierarchy and any edges that are incident on these nodes and are of the type
* requested by the "relationship" parameter.
*
* Nodes from the requested rank that do not have parents are assigned a root
* node in the output graph, which is set in the root graph attribute. This
* makes it easy to walk the hierarchy of movable nodes during ordering.
*
* Pre-conditions:
*
* 1. Input graph is a DAG
* 2. Base nodes in the input graph have a rank attribute
* 3. Subgraph nodes in the input graph has minRank and maxRank attributes
* 4. Edges have an assigned weight
*
* Post-conditions:
*
* 1. Output graph has all nodes in the movable rank with preserved
* hierarchy.
* 2. Root nodes in the movable layer are made children of the node
* indicated by the root attribute of the graph.
* 3. Non-movable nodes incident on movable nodes, selected by the
* relationship parameter, are included in the graph (without hierarchy).
* 4. Edges incident on movable nodes, selected by the relationship
* parameter, are added to the output graph.
* 5. The weights for copied edges are aggregated as need, since the output
* graph is not a multi-graph.
*/
function buildLayerGraph(g, rank, relationship) {
var root = createRootNode(g),
result = new Graph({ compound: true }).setGraph({ root: root })
.setDefaultNodeLabel(function(v) { return g.node(v); });
_.each(g.nodes(), function(v) {
var node = g.node(v),
parent = g.parent(v);
if (node.rank === rank || node.minRank <= rank && rank <= node.maxRank) {
result.setNode(v);
result.setParent(v, parent || root);
// This assumes we have only short edges!
_.each(g[relationship](v), function(e) {
var u = e.v === v ? e.w : e.v,
edge = result.edge(u, v),
weight = !_.isUndefined(edge) ? edge.weight : 0;
result.setEdge(u, v, { weight: g.edge(e).weight + weight });
});
if (_.has(node, "minRank")) {
result.setNode(v, {
borderLeft: node.borderLeft[rank],
borderRight: node.borderRight[rank]
});
}
}
});
return result;
}
function createRootNode(g) {
var v;
while (g.hasNode((v = _.uniqueId("_root"))));
return v;
}
},{"../graphlib":7,"../lodash":10}],16:[function(require,module,exports){
"use strict";
var _ = require("../lodash");
module.exports = crossCount;
/*
* A function that takes a layering (an array of layers, each with an array of
* ordererd nodes) and a graph and returns a weighted crossing count.
*
* Pre-conditions:
*
* 1. Input graph must be simple (not a multigraph), directed, and include
* only simple edges.
* 2. Edges in the input graph must have assigned weights.
*
* Post-conditions:
*
* 1. The graph and layering matrix are left unchanged.
*
* This algorithm is derived from Barth, et al., "Bilayer Cross Counting."
*/
function crossCount(g, layering) {
var cc = 0;
for (var i = 1; i < layering.length; ++i) {
cc += twoLayerCrossCount(g, layering[i-1], layering[i]);
}
return cc;
}
function twoLayerCrossCount(g, northLayer, southLayer) {
// Sort all of the edges between the north and south layers by their position
// in the north layer and then the south. Map these edges to the position of
// their head in the south layer.
var southPos = _.zipObject(southLayer,
_.map(southLayer, function (v, i) { return i; }));
var southEntries = _.flatten(_.map(northLayer, function(v) {
return _.chain(g.outEdges(v))
.map(function(e) {
return { pos: southPos[e.w], weight: g.edge(e).weight };
})
.sortBy("pos")
.value();
}), true);
// Build the accumulator tree
var firstIndex = 1;
while (firstIndex < southLayer.length) firstIndex <<= 1;
var treeSize = 2 * firstIndex - 1;
firstIndex -= 1;
var tree = _.map(new Array(treeSize), function() { return 0; });
// Calculate the weighted crossings
var cc = 0;
_.each(southEntries.forEach(function(entry) {
var index = entry.pos + firstIndex;
tree[index] += entry.weight;
var weightSum = 0;
while (index > 0) {
if (index % 2) {
weightSum += tree[index + 1];
}
index = (index - 1) >> 1;
tree[index] += entry.weight;
}
cc += entry.weight * weightSum;
}));
return cc;
}
},{"../lodash":10}],17:[function(require,module,exports){
"use strict";
var _ = require("../lodash"),
initOrder = require("./init-order"),
crossCount = require("./cross-count"),
sortSubgraph = require("./sort-subgraph"),
buildLayerGraph = require("./build-layer-graph"),
addSubgraphConstraints = require("./add-subgraph-constraints"),
Graph = require("../graphlib").Graph,
util = require("../util");
module.exports = order;
/*
* Applies heuristics to minimize edge crossings in the graph and sets the best
* order solution as an order attribute on each node.
*
* Pre-conditions:
*
* 1. Graph must be DAG
* 2. Graph nodes must be objects with a "rank" attribute
* 3. Graph edges must have the "weight" attribute
*
* Post-conditions:
*
* 1. Graph nodes will have an "order" attribute based on the results of the
* algorithm.
*/
function order(g) {
var maxRank = util.maxRank(g),
downLayerGraphs = buildLayerGraphs(g, _.range(1, maxRank + 1), "inEdges"),
upLayerGraphs = buildLayerGraphs(g, _.range(maxRank - 1, -1, -1), "outEdges");
var layering = initOrder(g);
assignOrder(g, layering);
var bestCC = Number.POSITIVE_INFINITY,
best;
for (var i = 0, lastBest = 0; lastBest < 4; ++i, ++lastBest) {
sweepLayerGraphs(i % 2 ? downLayerGraphs : upLayerGraphs, i % 4 >= 2);
layering = util.buildLayerMatrix(g);
var cc = crossCount(g, layering);
if (cc < bestCC) {
lastBest = 0;
best = _.cloneDeep(layering);
bestCC = cc;
}
}
assignOrder(g, best);
}
function buildLayerGraphs(g, ranks, relationship) {
return _.map(ranks, function(rank) {
return buildLayerGraph(g, rank, relationship);
});
}
function sweepLayerGraphs(layerGraphs, biasRight) {
var cg = new Graph();
_.each(layerGraphs, function(lg) {
var root = lg.graph().root;
var sorted = sortSubgraph(lg, root, cg, biasRight);
_.each(sorted.vs, function(v, i) {
lg.node(v).order = i;
});
addSubgraphConstraints(lg, cg, sorted.vs);
});
}
function assignOrder(g, layering) {
_.each(layering, function(layer) {
_.each(layer, function(v, i) {
g.node(v).order = i;
});
});
}
},{"../graphlib":7,"../lodash":10,"../util":29,"./add-subgraph-constraints":13,"./build-layer-graph":15,"./cross-count":16,"./init-order":18,"./sort-subgraph":20}],18:[function(require,module,exports){
"use strict";
var _ = require("../lodash");
module.exports = initOrder;
/*
* Assigns an initial order value for each node by performing a DFS search
* starting from nodes in the first rank. Nodes are assigned an order in their
* rank as they are first visited.
*
* This approach comes from Gansner, et al., "A Technique for Drawing Directed
* Graphs."
*
* Returns a layering matrix with an array per layer and each layer sorted by
* the order of its nodes.
*/
function initOrder(g) {
var visited = {},
simpleNodes = _.filter(g.nodes(), function(v) {
return !g.children(v).length;
}),
maxRank = _.max(_.map(simpleNodes, function(v) { return g.node(v).rank; })),
layers = _.map(_.range(maxRank + 1), function() { return []; });
function dfs(v) {
if (_.has(visited, v)) return;
visited[v] = true;
var node = g.node(v);
layers[node.rank].push(v);
_.each(g.successors(v), dfs);
}
var orderedVs = _.sortBy(simpleNodes, function(v) { return g.node(v).rank; });
_.each(orderedVs, dfs);
return layers;
}
},{"../lodash":10}],19:[function(require,module,exports){
"use strict";
var _ = require("../lodash");
module.exports = resolveConflicts;
/*
* Given a list of entries of the form {v, barycenter, weight} and a
* constraint graph this function will resolve any conflicts between the
* constraint graph and the barycenters for the entries. If the barycenters for
* an entry would violate a constraint in the constraint graph then we coalesce
* the nodes in the conflict into a new node that respects the contraint and
* aggregates barycenter and weight information.
*
* This implementation is based on the description in Forster, "A Fast and
* Simple Hueristic for Constrained Two-Level Crossing Reduction," thought it
* differs in some specific details.
*
* Pre-conditions:
*
* 1. Each entry has the form {v, barycenter, weight}, or if the node has
* no barycenter, then {v}.
*
* Returns:
*
* A new list of entries of the form {vs, i, barycenter, weight}. The list
* `vs` may either be a singleton or it may be an aggregation of nodes
* ordered such that they do not violate constraints from the constraint
* graph. The property `i` is the lowest original index of any of the
* elements in `vs`.
*/
function resolveConflicts(entries, cg) {
var mappedEntries = {};
_.each(entries, function(entry, i) {
var tmp = mappedEntries[entry.v] = {
indegree: 0,
"in": [],
out: [],
vs: [entry.v],
i: i
};
if (!_.isUndefined(entry.barycenter)) {
tmp.barycenter = entry.barycenter;
tmp.weight = entry.weight;
}
});
_.each(cg.edges(), function(e) {
var entryV = mappedEntries[e.v],
entryW = mappedEntries[e.w];
if (!_.isUndefined(entryV) && !_.isUndefined(entryW)) {
entryW.indegree++;
entryV.out.push(mappedEntries[e.w]);
}
});
var sourceSet = _.filter(mappedEntries, function(entry) {
return !entry.indegree;
});
return doResolveConflicts(sourceSet);
}
function doResolveConflicts(sourceSet) {
var entries = [];
function handleIn(vEntry) {
return function(uEntry) {
if (uEntry.merged) {
return;
}
if (_.isUndefined(uEntry.barycenter) ||
_.isUndefined(vEntry.barycenter) ||
uEntry.barycenter >= vEntry.barycenter) {
mergeEntries(vEntry, uEntry);
}
};
}
function handleOut(vEntry) {
return function(wEntry) {
wEntry["in"].push(vEntry);
if (--wEntry.indegree === 0) {
sourceSet.push(wEntry);
}
};
}
while (sourceSet.length) {
var entry = sourceSet.pop();
entries.push(entry);
_.each(entry["in"].reverse(), handleIn(entry));
_.each(entry.out, handleOut(entry));
}
return _.chain(entries)
.filter(function(entry) { return !entry.merged; })
.map(function(entry) {
return _.pick(entry, ["vs", "i", "barycenter", "weight"]);
})
.value();
}
function mergeEntries(target, source) {
var sum = 0,
weight = 0;
if (target.weight) {
sum += target.barycenter * target.weight;
weight += target.weight;
}
if (source.weight) {
sum += source.barycenter * source.weight;
weight += source.weight;
}
target.vs = source.vs.concat(target.vs);
target.barycenter = sum / weight;
target.weight = weight;
target.i = Math.min(source.i, target.i);
source.merged = true;
}
},{"../lodash":10}],20:[function(require,module,exports){
var _ = require("../lodash"),
barycenter = require("./barycenter"),
resolveConflicts = require("./resolve-conflicts"),
sort = require("./sort");
module.exports = sortSubgraph;
function sortSubgraph(g, v, cg, biasRight) {
var movable = g.children(v),
node = g.node(v),
bl = node ? node.borderLeft : undefined,
br = node ? node.borderRight: undefined,
subgraphs = {};
if (bl) {
movable = _.filter(movable, function(w) {
return w !== bl && w !== br;
});
}
var barycenters = barycenter(g, movable);
_.each(barycenters, function(entry) {
if (g.children(entry.v).length) {
var subgraphResult = sortSubgraph(g, entry.v, cg, biasRight);
subgraphs[entry.v] = subgraphResult;
if (_.has(subgraphResult, "barycenter")) {
mergeBarycenters(entry, subgraphResult);
}
}
});
var entries = resolveConflicts(barycenters, cg);
expandSubgraphs(entries, subgraphs);
var result = sort(entries, biasRight);
if (bl) {
result.vs = _.flatten([bl, result.vs, br], true);
if (g.predecessors(bl).length) {
var blPred = g.node(g.predecessors(bl)[0]),
brPred = g.node(g.predecessors(br)[0]);
if (!_.has(result, "barycenter")) {
result.barycenter = 0;
result.weight = 0;
}
result.barycenter = (result.barycenter * result.weight +
blPred.order + brPred.order) / (result.weight + 2);
result.weight += 2;
}
}
return result;
}
function expandSubgraphs(entries, subgraphs) {
_.each(entries, function(entry) {
entry.vs = _.flatten(entry.vs.map(function(v) {
if (subgraphs[v]) {
return subgraphs[v].vs;
}
return v;
}), true);
});
}
function mergeBarycenters(target, other) {
if (!_.isUndefined(target.barycenter)) {
target.barycenter = (target.barycenter * target.weight +
other.barycenter * other.weight) /
(target.weight + other.weight);
target.weight += other.weight;
} else {
target.barycenter = other.barycenter;
target.weight = other.weight;
}
}
},{"../lodash":10,"./barycenter":14,"./resolve-conflicts":19,"./sort":21}],21:[function(require,module,exports){
var _ = require("../lodash"),
util = require("../util");
module.exports = sort;
function sort(entries, biasRight) {
var parts = util.partition(entries, function(entry) {
return _.has(entry, "barycenter");
});
var sortable = parts.lhs,
unsortable = _.sortBy(parts.rhs, function(entry) { return -entry.i; }),
vs = [],
sum = 0,
weight = 0,
vsIndex = 0;
sortable.sort(compareWithBias(!!biasRight));
vsIndex = consumeUnsortable(vs, unsortable, vsIndex);
_.each(sortable, function (entry) {
vsIndex += entry.vs.length;
vs.push(entry.vs);
sum += entry.barycenter * entry.weight;
weight += entry.weight;
vsIndex = consumeUnsortable(vs, unsortable, vsIndex);
});
var result = { vs: _.flatten(vs, true) };
if (weight) {
result.barycenter = sum / weight;
result.weight = weight;
}
return result;
}
function consumeUnsortable(vs, unsortable, index) {
var last;
while (unsortable.length && (last = _.last(unsortable)).i <= index) {
unsortable.pop();
vs.push(last.vs);
index++;
}
return index;
}
function compareWithBias(bias) {
return function(entryV, entryW) {
if (entryV.barycenter < entryW.barycenter) {
return -1;
} else if (entryV.barycenter > entryW.barycenter) {
return 1;
}
return !bias ? entryV.i - entryW.i : entryW.i - entryV.i;
};
}
},{"../lodash":10,"../util":29}],22:[function(require,module,exports){
var _ = require("./lodash");
module.exports = parentDummyChains;
function parentDummyChains(g) {
var postorderNums = postorder(g);
_.each(g.graph().dummyChains, function(v) {
var node = g.node(v),
edgeObj = node.edgeObj,
pathData = findPath(g, postorderNums, edgeObj.v, edgeObj.w),
path = pathData.path,
lca = pathData.lca,
pathIdx = 0,
pathV = path[pathIdx],
ascending = true;
while (v !== edgeObj.w) {
node = g.node(v);
if (ascending) {
while ((pathV = path[pathIdx]) !== lca &&
g.node(pathV).maxRank < node.rank) {
pathIdx++;
}
if (pathV === lca) {
ascending = false;
}
}
if (!ascending) {
while (pathIdx < path.length - 1 &&
g.node(pathV = path[pathIdx + 1]).minRank <= node.rank) {
pathIdx++;
}
pathV = path[pathIdx];
}
g.setParent(v, pathV);
v = g.successors(v)[0];
}
});
}
// Find a path from v to w through the lowest common ancestor (LCA). Return the
// full path and the LCA.
function findPath(g, postorderNums, v, w) {
var vPath = [],
wPath = [],
low = Math.min(postorderNums[v].low, postorderNums[w].low),
lim = Math.max(postorderNums[v].lim, postorderNums[w].lim),
parent,
lca;
// Traverse up from v to find the LCA
parent = v;
do {
parent = g.parent(parent);
vPath.push(parent);
} while (parent &&
(postorderNums[parent].low > low || lim > postorderNums[parent].lim));
lca = parent;
// Traverse from w to LCA
parent = w;
while ((parent = g.parent(parent)) !== lca) {
wPath.push(parent);
}
return { path: vPath.concat(wPath.reverse()), lca: lca };
}
function postorder(g) {
var result = {},
lim = 0;
function dfs(v) {
var low = lim;
_.each(g.children(v), dfs);
result[v] = { low: low, lim: lim++ };
}
_.each(g.children(), dfs);
return result;
}
},{"./lodash":10}],23:[function(require,module,exports){
"use strict";
var _ = require("../lodash"),
Graph = require("../graphlib").Graph,
util = require("../util");
/*
* This module provides coordinate assignment based on Brandes and Köpf, "Fast
* and Simple Horizontal Coordinate Assignment."
*/
module.exports = {
positionX: positionX,
findType1Conflicts: findType1Conflicts,
findType2Conflicts: findType2Conflicts,
addConflict: addConflict,
hasConflict: hasConflict,
verticalAlignment: verticalAlignment,
horizontalCompaction: horizontalCompaction,
alignCoordinates: alignCoordinates,
findSmallestWidthAlignment: findSmallestWidthAlignment,
balance: balance
};
/*
* Marks all edges in the graph with a type-1 conflict with the "type1Conflict"
* property. A type-1 conflict is one where a non-inner segment crosses an
* inner segment. An inner segment is an edge with both incident nodes marked
* with the "dummy" property.
*
* This algorithm scans layer by layer, starting with the second, for type-1
* conflicts between the current layer and the previous layer. For each layer
* it scans the nodes from left to right until it reaches one that is incident
* on an inner segment. It then scans predecessors to determine if they have
* edges that cross that inner segment. At the end a final scan is done for all
* nodes on the current rank to see if they cross the last visited inner
* segment.
*
* This algorithm (safely) assumes that a dummy node will only be incident on a
* single node in the layers being scanned.
*/
function findType1Conflicts(g, layering) {
var conflicts = {};
function visitLayer(prevLayer, layer) {
var
// last visited node in the previous layer that is incident on an inner
// segment.
k0 = 0,
// Tracks the last node in this layer scanned for crossings with a type-1
// segment.
scanPos = 0,
prevLayerLength = prevLayer.length,
lastNode = _.last(layer);
_.each(layer, function(v, i) {
var w = findOtherInnerSegmentNode(g, v),
k1 = w ? g.node(w).order : prevLayerLength;
if (w || v === lastNode) {
_.each(layer.slice(scanPos, i +1), function(scanNode) {
_.each(g.predecessors(scanNode), function(u) {
var uLabel = g.node(u),
uPos = uLabel.order;
if ((uPos < k0 || k1 < uPos) &&
!(uLabel.dummy && g.node(scanNode).dummy)) {
addConflict(conflicts, u, scanNode);
}
});
});
scanPos = i + 1;
k0 = k1;
}
});
return layer;
}
_.reduce(layering, visitLayer);
return conflicts;
}
function findType2Conflicts(g, layering) {
var conflicts = {};
function scan(south, southPos, southEnd, prevNorthBorder, nextNorthBorder) {
var v;
_.each(_.range(southPos, southEnd), function(i) {
v = south[i];
if (g.node(v).dummy) {
_.each(g.predecessors(v), function(u) {
var uNode = g.node(u);
if (uNode.dummy &&
(uNode.order < prevNorthBorder || uNode.order > nextNorthBorder)) {
addConflict(conflicts, u, v);
}
});
}
});
}
function visitLayer(north, south) {
var prevNorthPos = -1,
nextNorthPos,
southPos = 0;
_.each(south, function(v, southLookahead) {
if (g.node(v).dummy === "border") {
var predecessors = g.predecessors(v);
if (predecessors.length) {
nextNorthPos = g.node(predecessors[0]).order;
scan(south, southPos, southLookahead, prevNorthPos, nextNorthPos);
southPos = southLookahead;
prevNorthPos = nextNorthPos;
}
}
scan(south, southPos, south.length, nextNorthPos, north.length);
});
return south;
}
_.reduce(layering, visitLayer);
return conflicts;
}
function findOtherInnerSegmentNode(g, v) {
if (g.node(v).dummy) {
return _.find(g.predecessors(v), function(u) {
return g.node(u).dummy;
});
}
}
function addConflict(conflicts, v, w) {
if (v > w) {
var tmp = v;
v = w;
w = tmp;
}
var conflictsV = conflicts[v];
if (!conflictsV) {
conflicts[v] = conflictsV = {};
}
conflictsV[w] = true;
}
function hasConflict(conflicts, v, w) {
if (v > w) {
var tmp = v;
v = w;
w = tmp;
}
return _.has(conflicts[v], w);
}
/*
* Try to align nodes into vertical "blocks" where possible. This algorithm
* attempts to align a node with one of its median neighbors. If the edge
* connecting a neighbor is a type-1 conflict then we ignore that possibility.
* If a previous node has already formed a block with a node after the node
* we're trying to form a block with, we also ignore that possibility - our
* blocks would be split in that scenario.
*/
function verticalAlignment(g, layering, conflicts, neighborFn) {
var root = {},
align = {},
pos = {};
// We cache the position here based on the layering because the graph and
// layering may be out of sync. The layering matrix is manipulated to
// generate different extreme alignments.
_.each(layering, function(layer) {
_.each(layer, function(v, order) {
root[v] = v;
align[v] = v;
pos[v] = order;
});
});
_.each(layering, function(layer) {
var prevIdx = -1;
_.each(layer, function(v) {
var ws = neighborFn(v);
if (ws.length) {
ws = _.sortBy(ws, function(w) { return pos[w]; });
var mp = (ws.length - 1) / 2;
for (var i = Math.floor(mp), il = Math.ceil(mp); i <= il; ++i) {
var w = ws[i];
if (align[v] === v &&
prevIdx < pos[w] &&
!hasConflict(conflicts, v, w)) {
align[w] = v;
align[v] = root[v] = root[w];
prevIdx = pos[w];
}
}
}
});
});
return { root: root, align: align };
}
function horizontalCompaction(g, layering, root, align, reverseSep) {
// This portion of the algorithm differs from BK due to a number of problems.
// Instead of their algorithm we construct a new block graph and do two
// sweeps. The first sweep places blocks with the smallest possible
// coordinates. The second sweep removes unused space by moving blocks to the
// greatest coordinates without violating separation.
var xs = {},
blockG = buildBlockGraph(g, layering, root, reverseSep);
// First pass, assign smallest coordinates via DFS
var visited = {};
function pass1(v) {
if (!_.has(visited, v)) {
visited[v] = true;
xs[v] = _.reduce(blockG.inEdges(v), function(max, e) {
pass1(e.v);
return Math.max(max, xs[e.v] + blockG.edge(e));
}, 0);
}
}
_.each(blockG.nodes(), pass1);
var borderType = reverseSep ? "borderLeft" : "borderRight";
function pass2(v) {
if (visited[v] !== 2) {
visited[v]++;
var node = g.node(v);
var min = _.reduce(blockG.outEdges(v), function(min, e) {
pass2(e.w);
return Math.min(min, xs[e.w] - blockG.edge(e));
}, Number.POSITIVE_INFINITY);
if (min !== Number.POSITIVE_INFINITY && node.borderType !== borderType) {
xs[v] = Math.max(xs[v], min);
}
}
}
_.each(blockG.nodes(), pass2);
// Assign x coordinates to all nodes
_.each(align, function(v) {
xs[v] = xs[root[v]];
});
return xs;
}
function buildBlockGraph(g, layering, root, reverseSep) {
var blockGraph = new Graph(),
graphLabel = g.graph(),
sepFn = sep(graphLabel.nodesep, graphLabel.edgesep, reverseSep);
_.each(layering, function(layer) {
var u;
_.each(layer, function(v) {
var vRoot = root[v];
blockGraph.setNode(vRoot);
if (u) {
var uRoot = root[u],
prevMax = blockGraph.edge(uRoot, vRoot);
blockGraph.setEdge(uRoot, vRoot, Math.max(sepFn(g, v, u), prevMax || 0));
}
u = v;
});
});
return blockGraph;
}
/*
* Returns the alignment that has the smallest width of the given alignments.
*/
function findSmallestWidthAlignment(g, xss) {
return _.min(xss, function(xs) {
var min = _.min(xs, function(x, v) { return x - width(g, v) / 2; }),
max = _.max(xs, function(x, v) { return x + width(g, v) / 2; });
return max - min;
});
}
/*
* Align the coordinates of each of the layout alignments such that
* left-biased alignments have their minimum coordinate at the same point as
* the minimum coordinate of the smallest width alignment and right-biased
* alignments have their maximum coordinate at the same point as the maximum
* coordinate of the smallest width alignment.
*/
function alignCoordinates(xss, alignTo) {
var alignToMin = _.min(alignTo),
alignToMax = _.max(alignTo);
_.each(["u", "d"], function(vert) {
_.each(["l", "r"], function(horiz) {
var alignment = vert + horiz,
xs = xss[alignment],
delta;
if (xs === alignTo) return;
delta = horiz === "l" ? alignToMin - _.min(xs) : alignToMax - _.max(xs);
if (delta) {
xss[alignment] = _.mapValues(xs, function(x) { return x + delta; });
}
});
});
}
function balance(xss, align) {
return _.mapValues(xss.ul, function(ignore, v) {
if (align) {
return xss[align.toLowerCase()][v];
} else {
var xs = _.sortBy(_.pluck(xss, v));
return (xs[1] + xs[2]) / 2;
}
});
}
function positionX(g) {
var layering = util.buildLayerMatrix(g),
conflicts = _.merge(findType1Conflicts(g, layering),
findType2Conflicts(g, layering));
var xss = {},
adjustedLayering;
_.each(["u", "d"], function(vert) {
adjustedLayering = vert === "u" ? layering : _.values(layering).reverse();
_.each(["l", "r"], function(horiz) {
if (horiz === "r") {
adjustedLayering = _.map(adjustedLayering, function(inner) {
return _.values(inner).reverse();
});
}
var neighborFn = _.bind(vert === "u" ? g.predecessors : g.successors, g);
var align = verticalAlignment(g, adjustedLayering, conflicts, neighborFn);
var xs = horizontalCompaction(g, adjustedLayering,
align.root, align.align,
horiz === "r");
if (horiz === "r") {
xs = _.mapValues(xs, function(x) { return -x; });
}
xss[vert + horiz] = xs;
});
});
var smallestWidth = findSmallestWidthAlignment(g, xss);
alignCoordinates(xss, smallestWidth);
return balance(xss, g.graph().align);
}
function sep(nodeSep, edgeSep, reverseSep) {
return function(g, v, w) {
var vLabel = g.node(v),
wLabel = g.node(w),
sum = 0,
delta;
sum += vLabel.width / 2;
if (_.has(vLabel, "labelpos")) {
switch (vLabel.labelpos.toLowerCase()) {
case "l": delta = -vLabel.width / 2; break;
case "r": delta = vLabel.width / 2; break;
}
}
if (delta) {
sum += reverseSep ? delta : -delta;
}
delta = 0;
sum += (vLabel.dummy ? edgeSep : nodeSep) / 2;
sum += (wLabel.dummy ? edgeSep : nodeSep) / 2;
sum += wLabel.width / 2;
if (_.has(wLabel, "labelpos")) {
switch (wLabel.labelpos.toLowerCase()) {
case "l": delta = wLabel.width / 2; break;
case "r": delta = -wLabel.width / 2; break;
}
}
if (delta) {
sum += reverseSep ? delta : -delta;
}
delta = 0;
return sum;
};
}
function width(g, v) {
return g.node(v).width;
}
},{"../graphlib":7,"../lodash":10,"../util":29}],24:[function(require,module,exports){
"use strict";
var _ = require("../lodash"),
util = require("../util"),
positionX = require("./bk").positionX;
module.exports = position;
function position(g) {
g = util.asNonCompoundGraph(g);
positionY(g);
_.each(positionX(g), function(x, v) {
g.node(v).x = x;
});
}
function positionY(g) {
var layering = util.buildLayerMatrix(g),
rankSep = g.graph().ranksep,
prevY = 0;
_.each(layering, function(layer) {
var maxHeight = _.max(_.map(layer, function(v) { return g.node(v).height; }));
_.each(layer, function(v) {
g.node(v).y = prevY + maxHeight / 2;
});
prevY += maxHeight + rankSep;
});
}
},{"../lodash":10,"../util":29,"./bk":23}],25:[function(require,module,exports){
"use strict";
var _ = require("../lodash"),
Graph = require("../graphlib").Graph,
slack = require("./util").slack;
module.exports = feasibleTree;
/*
* Constructs a spanning tree with tight edges and adjusted the input node's
* ranks to achieve this. A tight edge is one that is has a length that matches
* its "minlen" attribute.
*
* The basic structure for this function is derived from Gansner, et al., "A
* Technique for Drawing Directed Graphs."
*
* Pre-conditions:
*
* 1. Graph must be a DAG.
* 2. Graph must be connected.
* 3. Graph must have at least one node.
* 5. Graph nodes must have been previously assigned a "rank" property that
* respects the "minlen" property of incident edges.
* 6. Graph edges must have a "minlen" property.
*
* Post-conditions:
*
* - Graph nodes will have their rank adjusted to ensure that all edges are
* tight.
*
* Returns a tree (undirected graph) that is constructed using only "tight"
* edges.
*/
function feasibleTree(g) {
var t = new Graph({ directed: false });
// Choose arbitrary node from which to start our tree
var start = g.nodes()[0],
size = g.nodeCount();
t.setNode(start, {});
var edge, delta;
while (tightTree(t, g) < size) {
edge = findMinSlackEdge(t, g);
delta = t.hasNode(edge.v) ? slack(g, edge) : -slack(g, edge);
shiftRanks(t, g, delta);
}
return t;
}
/*
* Finds a maximal tree of tight edges and returns the number of nodes in the
* tree.
*/
function tightTree(t, g) {
function dfs(v) {
_.each(g.nodeEdges(v), function(e) {
var edgeV = e.v,
w = (v === edgeV) ? e.w : edgeV;
if (!t.hasNode(w) && !slack(g, e)) {
t.setNode(w, {});
t.setEdge(v, w, {});
dfs(w);
}
});
}
_.each(t.nodes(), dfs);
return t.nodeCount();
}
/*
* Finds the edge with the smallest slack that is incident on tree and returns
* it.
*/
function findMinSlackEdge(t, g) {
return _.min(g.edges(), function(e) {
if (t.hasNode(e.v) !== t.hasNode(e.w)) {
return slack(g, e);
}
});
}
function shiftRanks(t, g, delta) {
_.each(t.nodes(), function(v) {
g.node(v).rank += delta;
});
}
},{"../graphlib":7,"../lodash":10,"./util":28}],26:[function(require,module,exports){
"use strict";
var rankUtil = require("./util"),
longestPath = rankUtil.longestPath,
feasibleTree = require("./feasible-tree"),
networkSimplex = require("./network-simplex");
module.exports = rank;
/*
* Assigns a rank to each node in the input graph that respects the "minlen"
* constraint specified on edges between nodes.
*
* This basic structure is derived from Gansner, et al., "A Technique for
* Drawing Directed Graphs."
*
* Pre-conditions:
*
* 1. Graph must be a connected DAG
* 2. Graph nodes must be objects
* 3. Graph edges must have "weight" and "minlen" attributes
*
* Post-conditions:
*
* 1. Graph nodes will have a "rank" attribute based on the results of the
* algorithm. Ranks can start at any index (including negative), we'll
* fix them up later.
*/
function rank(g) {
switch(g.graph().ranker) {
case "network-simplex": networkSimplexRanker(g); break;
case "tight-tree": tightTreeRanker(g); break;
case "longest-path": longestPathRanker(g); break;
default: networkSimplexRanker(g);
}
}
// A fast and simple ranker, but results are far from optimal.
var longestPathRanker = longestPath;
function tightTreeRanker(g) {
longestPath(g);
feasibleTree(g);
}
function networkSimplexRanker(g) {
networkSimplex(g);
}
},{"./feasible-tree":25,"./network-simplex":27,"./util":28}],27:[function(require,module,exports){
"use strict";
var _ = require("../lodash"),
feasibleTree = require("./feasible-tree"),
slack = require("./util").slack,
initRank = require("./util").longestPath,
preorder = require("../graphlib").alg.preorder,
postorder = require("../graphlib").alg.postorder,
simplify = require("../util").simplify;
module.exports = networkSimplex;
// Expose some internals for testing purposes
networkSimplex.initLowLimValues = initLowLimValues;
networkSimplex.initCutValues = initCutValues;
networkSimplex.calcCutValue = calcCutValue;
networkSimplex.leaveEdge = leaveEdge;
networkSimplex.enterEdge = enterEdge;
networkSimplex.exchangeEdges = exchangeEdges;
/*
* The network simplex algorithm assigns ranks to each node in the input graph
* and iteratively improves the ranking to reduce the length of edges.
*
* Preconditions:
*
* 1. The input graph must be a DAG.
* 2. All nodes in the graph must have an object value.
* 3. All edges in the graph must have "minlen" and "weight" attributes.
*
* Postconditions:
*
* 1. All nodes in the graph will have an assigned "rank" attribute that has
* been optimized by the network simplex algorithm. Ranks start at 0.
*
*
* A rough sketch of the algorithm is as follows:
*
* 1. Assign initial ranks to each node. We use the longest path algorithm,
* which assigns ranks to the lowest position possible. In general this
* leads to very wide bottom ranks and unnecessarily long edges.
* 2. Construct a feasible tight tree. A tight tree is one such that all
* edges in the tree have no slack (difference between length of edge
* and minlen for the edge). This by itself greatly improves the assigned
* rankings by shorting edges.
* 3. Iteratively find edges that have negative cut values. Generally a
* negative cut value indicates that the edge could be removed and a new
* tree edge could be added to produce a more compact graph.
*
* Much of the algorithms here are derived from Gansner, et al., "A Technique
* for Drawing Directed Graphs." The structure of the file roughly follows the
* structure of the overall algorithm.
*/
function networkSimplex(g) {
g = simplify(g);
initRank(g);
var t = feasibleTree(g);
initLowLimValues(t);
initCutValues(t, g);
var e, f;
while ((e = leaveEdge(t))) {
f = enterEdge(t, g, e);
exchangeEdges(t, g, e, f);
}
}
/*
* Initializes cut values for all edges in the tree.
*/
function initCutValues(t, g) {
var vs = postorder(t, t.nodes());
vs = vs.slice(0, vs.length - 1);
_.each(vs, function(v) {
assignCutValue(t, g, v);
});
}
function assignCutValue(t, g, child) {
var childLab = t.node(child),
parent = childLab.parent;
t.edge(child, parent).cutvalue = calcCutValue(t, g, child);
}
/*
* Given the tight tree, its graph, and a child in the graph calculate and
* return the cut value for the edge between the child and its parent.
*/
function calcCutValue(t, g, child) {
var childLab = t.node(child),
parent = childLab.parent,
// True if the child is on the tail end of the edge in the directed graph
childIsTail = true,
// The graph's view of the tree edge we're inspecting
graphEdge = g.edge(child, parent),
// The accumulated cut value for the edge between this node and its parent
cutValue = 0;
if (!graphEdge) {
childIsTail = false;
graphEdge = g.edge(parent, child);
}
cutValue = graphEdge.weight;
_.each(g.nodeEdges(child), function(e) {
var isOutEdge = e.v === child,
other = isOutEdge ? e.w : e.v;
if (other !== parent) {
var pointsToHead = isOutEdge === childIsTail,
otherWeight = g.edge(e).weight;
cutValue += pointsToHead ? otherWeight : -otherWeight;
if (isTreeEdge(t, child, other)) {
var otherCutValue = t.edge(child, other).cutvalue;
cutValue += pointsToHead ? -otherCutValue : otherCutValue;
}
}
});
return cutValue;
}
function initLowLimValues(tree, root) {
if (arguments.length < 2) {
root = tree.nodes()[0];
}
dfsAssignLowLim(tree, {}, 1, root);
}
function dfsAssignLowLim(tree, visited, nextLim, v, parent) {
var low = nextLim,
label = tree.node(v);
visited[v] = true;
_.each(tree.neighbors(v), function(w) {
if (!_.has(visited, w)) {
nextLim = dfsAssignLowLim(tree, visited, nextLim, w, v);
}
});
label.low = low;
label.lim = nextLim++;
if (parent) {
label.parent = parent;
} else {
// TODO should be able to remove this when we incrementally update low lim
delete label.parent;
}
return nextLim;
}
function leaveEdge(tree) {
return _.find(tree.edges(), function(e) {
return tree.edge(e).cutvalue < 0;
});
}
function enterEdge(t, g, edge) {
var v = edge.v,
w = edge.w;
// For the rest of this function we assume that v is the tail and w is the
// head, so if we don't have this edge in the graph we should flip it to
// match the correct orientation.
if (!g.hasEdge(v, w)) {
v = edge.w;
w = edge.v;
}
var vLabel = t.node(v),
wLabel = t.node(w),
tailLabel = vLabel,
flip = false;
// If the root is in the tail of the edge then we need to flip the logic that
// checks for the head and tail nodes in the candidates function below.
if (vLabel.lim > wLabel.lim) {
tailLabel = wLabel;
flip = true;
}
var candidates = _.filter(g.edges(), function(edge) {
return flip === isDescendant(t, t.node(edge.v), tailLabel) &&
flip !== isDescendant(t, t.node(edge.w), tailLabel);
});
return _.min(candidates, function(edge) { return slack(g, edge); });
}
function exchangeEdges(t, g, e, f) {
var v = e.v,
w = e.w;
t.removeEdge(v, w);
t.setEdge(f.v, f.w, {});
initLowLimValues(t);
initCutValues(t, g);
updateRanks(t, g);
}
function updateRanks(t, g) {
var root = _.find(t.nodes(), function(v) { return !g.node(v).parent; }),
vs = preorder(t, root);
vs = vs.slice(1);
_.each(vs, function(v) {
var parent = t.node(v).parent,
edge = g.edge(v, parent),
flipped = false;
if (!edge) {
edge = g.edge(parent, v);
flipped = true;
}
g.node(v).rank = g.node(parent).rank + (flipped ? edge.minlen : -edge.minlen);
});
}
/*
* Returns true if the edge is in the tree.
*/
function isTreeEdge(tree, u, v) {
return tree.hasEdge(u, v);
}
/*
* Returns true if the specified node is descendant of the root node per the
* assigned low and lim attributes in the tree.
*/
function isDescendant(tree, vLabel, rootLabel) {
return rootLabel.low <= vLabel.lim && vLabel.lim <= rootLabel.lim;
}
},{"../graphlib":7,"../lodash":10,"../util":29,"./feasible-tree":25,"./util":28}],28:[function(require,module,exports){
"use strict";
var _ = require("../lodash");
module.exports = {
longestPath: longestPath,
slack: slack
};
/*
* Initializes ranks for the input graph using the longest path algorithm. This
* algorithm scales well and is fast in practice, it yields rather poor
* solutions. Nodes are pushed to the lowest layer possible, leaving the bottom
* ranks wide and leaving edges longer than necessary. However, due to its
* speed, this algorithm is good for getting an initial ranking that can be fed
* into other algorithms.
*
* This algorithm does not normalize layers because it will be used by other
* algorithms in most cases. If using this algorithm directly, be sure to
* run normalize at the end.
*
* Pre-conditions:
*
* 1. Input graph is a DAG.
* 2. Input graph node labels can be assigned properties.
*
* Post-conditions:
*
* 1. Each node will be assign an (unnormalized) "rank" property.
*/
function longestPath(g) {
var visited = {};
function dfs(v) {
var label = g.node(v);
if (_.has(visited, v)) {
return label.rank;
}
visited[v] = true;
var rank = _.min(_.map(g.outEdges(v), function(e) {
return dfs(e.w) - g.edge(e).minlen;
}));
if (rank === Number.POSITIVE_INFINITY) {
rank = 0;
}
return (label.rank = rank);
}
_.each(g.sources(), dfs);
}
/*
* Returns the amount of slack for the given edge. The slack is defined as the
* difference between the length of the edge and its minimum length.
*/
function slack(g, e) {
return g.node(e.w).rank - g.node(e.v).rank - g.edge(e).minlen;
}
},{"../lodash":10}],29:[function(require,module,exports){
"use strict";
var _ = require("./lodash"),
Graph = require("./graphlib").Graph;
module.exports = {
addDummyNode: addDummyNode,
simplify: simplify,
asNonCompoundGraph: asNonCompoundGraph,
successorWeights: successorWeights,
predecessorWeights: predecessorWeights,
intersectRect: intersectRect,
buildLayerMatrix: buildLayerMatrix,
normalizeRanks: normalizeRanks,
removeEmptyRanks: removeEmptyRanks,
addBorderNode: addBorderNode,
maxRank: maxRank,
partition: partition,
time: time,
notime: notime
};
/*
* Adds a dummy node to the graph and return v.
*/
function addDummyNode(g, type, attrs, name) {
var v;
do {
v = _.uniqueId(name);
} while (g.hasNode(v));
attrs.dummy = type;
g.setNode(v, attrs);
return v;
}
/*
* Returns a new graph with only simple edges. Handles aggregation of data
* associated with multi-edges.
*/
function simplify(g) {
var simplified = new Graph().setGraph(g.graph());
_.each(g.nodes(), function(v) { simplified.setNode(v, g.node(v)); });
_.each(g.edges(), function(e) {
var simpleLabel = simplified.edge(e.v, e.w) || { weight: 0, minlen: 1 },
label = g.edge(e);
simplified.setEdge(e.v, e.w, {
weight: simpleLabel.weight + label.weight,
minlen: Math.max(simpleLabel.minlen, label.minlen)
});
});
return simplified;
}
function asNonCompoundGraph(g) {
var simplified = new Graph({ multigraph: g.isMultigraph() }).setGraph(g.graph());
_.each(g.nodes(), function(v) {
if (!g.children(v).length) {
simplified.setNode(v, g.node(v));
}
});
_.each(g.edges(), function(e) {
simplified.setEdge(e, g.edge(e));
});
return simplified;
}
function successorWeights(g) {
var weightMap = _.map(g.nodes(), function(v) {
var sucs = {};
_.each(g.outEdges(v), function(e) {
sucs[e.w] = (sucs[e.w] || 0) + g.edge(e).weight;
});
return sucs;
});
return _.zipObject(g.nodes(), weightMap);
}
function predecessorWeights(g) {
var weightMap = _.map(g.nodes(), function(v) {
var preds = {};
_.each(g.inEdges(v), function(e) {
preds[e.v] = (preds[e.v] || 0) + g.edge(e).weight;
});
return preds;
});
return _.zipObject(g.nodes(), weightMap);
}
/*
* Finds where a line starting at point ({x, y}) would intersect a rectangle
* ({x, y, width, height}) if it were pointing at the rectangle's center.
*/
function intersectRect(rect, point) {
var x = rect.x;
var y = rect.y;
// Rectangle intersection algorithm from:
// http://math.stackexchange.com/questions/108113/find-edge-between-two-boxes
var dx = point.x - x;
var dy = point.y - y;
var w = rect.width / 2;
var h = rect.height / 2;
if (!dx && !dy) {
throw new Error("Not possible to find intersection inside of the rectangle");
}
var sx, sy;
if (Math.abs(dy) * w > Math.abs(dx) * h) {
// Intersection is top or bottom of rect.
if (dy < 0) {
h = -h;
}
sx = h * dx / dy;
sy = h;
} else {
// Intersection is left or right of rect.
if (dx < 0) {
w = -w;
}
sx = w;
sy = w * dy / dx;
}
return { x: x + sx, y: y + sy };
}
/*
* Given a DAG with each node assigned "rank" and "order" properties, this
* function will produce a matrix with the ids of each node.
*/
function buildLayerMatrix(g) {
var layering = _.map(_.range(maxRank(g) + 1), function() { return []; });
_.each(g.nodes(), function(v) {
var node = g.node(v),
rank = node.rank;
if (!_.isUndefined(rank)) {
layering[rank][node.order] = v;
}
});
return layering;
}
/*
* Adjusts the ranks for all nodes in the graph such that all nodes v have
* rank(v) >= 0 and at least one node w has rank(w) = 0.
*/
function normalizeRanks(g) {
var min = _.min(_.map(g.nodes(), function(v) { return g.node(v).rank; }));
_.each(g.nodes(), function(v) {
var node = g.node(v);
if (_.has(node, "rank")) {
node.rank -= min;
}
});
}
function removeEmptyRanks(g) {
// Ranks may not start at 0, so we need to offset them
var offset = _.min(_.map(g.nodes(), function(v) { return g.node(v).rank; }));
var layers = [];
_.each(g.nodes(), function(v) {
var rank = g.node(v).rank - offset;
if (!layers[rank]) {
layers[rank] = [];
}
layers[rank].push(v);
});
var delta = 0,
nodeRankFactor = g.graph().nodeRankFactor;
_.each(layers, function(vs, i) {
if (_.isUndefined(vs) && i % nodeRankFactor !== 0) {
--delta;
} else if (delta) {
_.each(vs, function(v) { g.node(v).rank += delta; });
}
});
}
function addBorderNode(g, prefix, rank, order) {
var node = {
width: 0,
height: 0
};
if (arguments.length >= 4) {
node.rank = rank;
node.order = order;
}
return addDummyNode(g, "border", node, prefix);
}
function maxRank(g) {
return _.max(_.map(g.nodes(), function(v) {
var rank = g.node(v).rank;
if (!_.isUndefined(rank)) {
return rank;
}
}));
}
/*
* Partition a collection into two groups: `lhs` and `rhs`. If the supplied
* function returns true for an entry it goes into `lhs`. Otherwise it goes
* into `rhs.
*/
function partition(collection, fn) {
var result = { lhs: [], rhs: [] };
_.each(collection, function(value) {
if (fn(value)) {
result.lhs.push(value);
} else {
result.rhs.push(value);
}
});
return result;
}
/*
* Returns a new function that wraps `fn` with a timer. The wrapper logs the
* time it takes to execute the function.
*/
function time(name, fn) {
var start = _.now();
try {
return fn();
} finally {
console.log(name + " time: " + (_.now() - start) + "ms");
}
}
function notime(name, fn) {
return fn();
}
},{"./graphlib":7,"./lodash":10}],30:[function(require,module,exports){
module.exports = "0.7.4";
},{}]},{},[1])(1)
});
