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/*
* (C) Copyright 2018-2023, by Assaf Mizrachi and Contributors.
*
* JGraphT : a free Java graph-theory library
*
* See the CONTRIBUTORS.md file distributed with this work for additional
* information regarding copyright ownership.
*
* This program and the accompanying materials are made available under the
* terms of the Eclipse Public License 2.0 which is available at
* http://www.eclipse.org/legal/epl-2.0, or the
* GNU Lesser General Public License v2.1 or later
* which is available at
* http://www.gnu.org/licenses/old-licenses/lgpl-2.1-standalone.html.
*
* SPDX-License-Identifier: EPL-2.0 OR LGPL-2.1-or-later
*/
package org.jgrapht.alg.shortestpath;
import org.jgrapht.*;
import org.jgrapht.alg.interfaces.*;
import org.jgrapht.alg.util.*;
import org.jgrapht.graph.*;
import java.util.*;
import java.util.stream.*;
/**
* A base implementation of a $k$ disjoint shortest paths algorithm based on the strategy used in
* Suurballe and Bhandari algorithms. The algorithm procedure goes as follow:
*
* - Using some known shortest path algorithm (e.g. Dijkstra) to find the shortest path $P_1$ from
* source to target.
*
- For i = 2,...,$k$
*
- Perform some graph transformations based on the previously found path
*
- Find the shortest path $P_i$ from source to target
*
- Remove all overlapping edges to get $k$ disjoint paths.
*
* The class implements the above procedure and resolves final paths (step 5) from the intermediate
* path results found in step 4. An extending class has to implement two methods:
*
* - {@link #transformGraph} - to be used in step 3.
*
- {@link #calculateShortestPath} - to be used in step 4.
*
* Currently known extensions are {@link SuurballeKDisjointShortestPaths} and
* {@link BhandariKDisjointShortestPaths}.
*
* @param the graph vertex type
* @param the graph edge type
*
* @author Assaf Mizrachi
* @author Benjamin Krogh
*/
abstract class BaseKDisjointShortestPathsAlgorithm
implements KShortestPathAlgorithm
{
/**
* Graph on which shortest paths are searched.
*/
protected Graph workingGraph;
protected List> pathList;
protected Graph originalGraph;
private Set validEdges;
/**
* Creates a new instance of the algorithm
*
* @param graph graph on which shortest paths are searched.
*
* @throws IllegalArgumentException if the graph is null.
* @throws IllegalArgumentException if the graph is undirected.
* @throws IllegalArgumentException if the graph is not simple.
*/
public BaseKDisjointShortestPathsAlgorithm(Graph graph)
{
this.originalGraph = graph;
GraphTests.requireDirected(graph);
if (!GraphTests.isSimple(graph)) {
throw new IllegalArgumentException("Graph must be simple");
}
}
/**
* Returns the $k$ shortest simple paths in increasing order of weight.
*
* @param startVertex source vertex of the calculated paths.
* @param endVertex target vertex of the calculated paths.
*
* @return list of disjoint paths between the start vertex and the end vertex
*
* @throws IllegalArgumentException if the graph does not contain the startVertex or the
* endVertex
* @throws IllegalArgumentException if the startVertex and the endVertex are the same vertices
* @throws IllegalArgumentException if the startVertex or the endVertex is null
*/
@Override
public List> getPaths(V startVertex, V endVertex, int k)
{
if (k <= 0) {
throw new IllegalArgumentException("Number of paths must be positive");
}
Objects.requireNonNull(startVertex, "startVertex is null");
Objects.requireNonNull(endVertex, "endVertex is null");
if (endVertex.equals(startVertex)) {
throw new IllegalArgumentException("The end vertex is the same as the start vertex!");
}
if (!originalGraph.containsVertex(startVertex)) {
throw new IllegalArgumentException("graph must contain the start vertex!");
}
if (!originalGraph.containsVertex(endVertex)) {
throw new IllegalArgumentException("graph must contain the end vertex!");
}
// Create a working graph copy to avoid modifying the underlying graph. This gets
// reinitialized for every call to getPaths since previous calls may have modified it. Since
// the original graph may be using intrusive edges, we have to use an AsWeightedGraph view
// (even when the graph copy is already weighted) to avoid writing weight changes through to
// the underlying graph.
this.workingGraph = new AsWeightedGraph<>(
new DefaultDirectedWeightedGraph<>(
this.originalGraph.getVertexSupplier(), this.originalGraph.getEdgeSupplier()),
new HashMap<>(), false);
Graphs.addGraph(workingGraph, this.originalGraph);
this.pathList = new ArrayList<>();
GraphPath currentPath = calculateShortestPath(startVertex, endVertex);
if (currentPath != null) {
pathList.add(currentPath.getEdgeList());
for (int i = 0; i < k - 1; i++) {
transformGraph(this.pathList.get(i));
currentPath = calculateShortestPath(startVertex, endVertex);
if (currentPath != null) {
pathList.add(currentPath.getEdgeList());
} else {
break;
}
}
}
return pathList.size() > 0 ? resolvePaths(startVertex, endVertex) : Collections.emptyList();
}
/**
* At the end of the search we have list of intermediate paths - not necessarily disjoint and
* may contain reversed edges. Here we go over all, removing overlapping edges and merging them
* to valid paths (from start to end). Finally, we sort them according to their weight.
*
* @param startVertex the start vertex
* @param endVertex the end vertex
*
* @return sorted list of disjoint paths from start vertex to end vertex.
*/
private List> resolvePaths(V startVertex, V endVertex)
{
// first we need to remove overlapping edges.
findValidEdges();
// now we might be left with path fragments (not necessarily leading from start to end).
// We need to merge them to valid paths.
List> paths = buildPaths(startVertex, endVertex);
// sort paths by overall weight (ascending)
Collections.sort(paths, Comparator.comparingDouble(GraphPath::getWeight));
return paths;
}
/**
* After removing overlapping edges, each path is not necessarily connecting start to end
* vertex. Here we connect the path fragments to valid paths (from start to end).
*
* @param startVertex the start vertex
* @param endVertex the end vertex
*
* @return list of disjoint paths from start to end.
*/
private List> buildPaths(V startVertex, V endVertex)
{
Map> sourceVertexToEdge = this.validEdges.stream().collect(
Collectors.groupingBy(this::getEdgeSource, Collectors.toCollection(ArrayDeque::new)));
ArrayDeque startEdges = sourceVertexToEdge.get(startVertex);
List> result = new ArrayList<>();
for (E edge : startEdges) {
final List resultPath = new ArrayList<>();
resultPath.add(edge);
while (true) {
final V edgeTarget = getEdgeTarget(edge);
if (edgeTarget.equals(endVertex)) {
break;
}
ArrayDeque outgoingEdges = sourceVertexToEdge.get(edgeTarget);
edge = outgoingEdges.poll();
resultPath.add(edge);
}
GraphPath graphPath = createGraphPath(resultPath, startVertex, endVertex);
result.add(graphPath);
}
return result;
}
/**
* Iterate over all paths and remove all edges used an even number of times. The remaining edges
* forms the valid edge set, which is used in the buildPaths method to construct the k-shortest
* paths
*/
private void findValidEdges()
{
Map, E> validEdges = new LinkedHashMap<>();
for (List path : pathList) {
for (E e : path) {
V v = this.getEdgeSource(e);
V u = this.getEdgeTarget(e);
UnorderedPair edgePair = new UnorderedPair<>(v, u);
validEdges.compute(edgePair, (unused, edge) -> edge == null ? e : null);
}
}
this.validEdges = new LinkedHashSet<>(validEdges.values());
}
private GraphPath createGraphPath(List edgeList, V startVertex, V endVertex)
{
double weight = 0;
for (E edge : edgeList) {
weight += originalGraph.getEdgeWeight(edge);
}
return new GraphWalk<>(originalGraph, startVertex, endVertex, edgeList, weight);
}
private V getEdgeSource(E e)
{
return this.workingGraph.containsEdge(e) ? this.workingGraph.getEdgeSource(e)
: this.originalGraph.getEdgeSource(e);
}
private V getEdgeTarget(E e)
{
return this.workingGraph.containsEdge(e) ? this.workingGraph.getEdgeTarget(e)
: this.originalGraph.getEdgeTarget(e);
}
/**
* Calculates the shortest paths for the current iteration. Path is not final; rather, it is
* intended to be used in a "post-production" phase (see resolvePaths method).
*
* @param startVertex the start vertex
* @param endVertex the end vertex
*
* @return the shortest path between start and end vertices.
*/
protected abstract GraphPath calculateShortestPath(V startVertex, V endVertex);
/**
* Prepares the working graph for next iteration. To be called from the second iteration and on
* so implementation may assume a preceding {@link #calculateShortestPath} call.
*
* @param previousPath the path found at the previous iteration.
*/
protected abstract void transformGraph(List previousPath);
}