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package graphql.schema.diffing;

import com.google.common.collect.HashMultiset;
import com.google.common.collect.Multiset;
import com.google.common.collect.Multisets;
import graphql.Internal;

import java.util.ArrayList;
import java.util.Collection;
import java.util.LinkedHashMap;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.concurrent.LinkedBlockingQueue;
import java.util.concurrent.atomic.AtomicInteger;

import static graphql.Assert.assertFalse;
import static graphql.Assert.assertTrue;
import static graphql.schema.diffing.EditorialCostForMapping.baseEditorialCostForMapping;
import static graphql.schema.diffing.EditorialCostForMapping.editorialCostForMapping;

/**
 * This is an algorithm calculating the optimal edit to change the source graph into the target graph.
 * 

* It is based on the following two papers (both papers are from the same authors. The first one is newer, but the older one is more detailed in some aspects) *

* Accelerating Graph Similarity Search via Efficient GED Computation (https://lijunchang.github.io/pdf/2022-ged-tkde.pdf) *

* Efficient Graph Edit Distance Computation and Verification via Anchor-aware Lower Bound Estimation (https://arxiv.org/abs/1709.06810) *

* The algorithm is a modified version of "AStar-BMao". * It is adapted to directed graphs as a GraphQL schema is most naturally represented as directed graph (vs the undirected graphs used in the papers). */ @Internal public class DiffImpl { private final PossibleMappingsCalculator possibleMappingsCalculator; private final SchemaGraph completeSourceGraph; private final SchemaGraph completeTargetGraph; private final PossibleMappingsCalculator.PossibleMappings possibleMappings; private final SchemaDiffingRunningCheck runningCheck; private static class MappingEntry { public LinkedBlockingQueue mappingEntriesSiblings = new LinkedBlockingQueue<>(); public int[] assignments; /** * These are the available vertices, relative to the parent mapping. * Meaning the last mapped element is NOT contained in it. */ public List availableTargetVertices; Mapping partialMapping; int level; // = partialMapping.size double lowerBoundCost; public MappingEntry(Mapping partialMapping, int level, double lowerBoundCost) { this.partialMapping = partialMapping; this.level = level; this.lowerBoundCost = lowerBoundCost; } } /** * An optimal edit from one graph to another. * The mapping maps all vertices from source to target, but * not all mappings represent an actual change. This is why there is a separate list * of the actual changes. */ public static class OptimalEdit { private final SchemaGraph completeSourceGraph; private final SchemaGraph completeTargetGraph; public Mapping mapping; public int ged = Integer.MAX_VALUE; public OptimalEdit( SchemaGraph completeSourceGraph, SchemaGraph completeTargetGraph) { this.completeSourceGraph = completeSourceGraph; this.completeTargetGraph = completeTargetGraph; } public OptimalEdit( SchemaGraph completeSourceGraph, SchemaGraph completeTargetGraph, Mapping mapping, int ged) { this.completeSourceGraph = completeSourceGraph; this.completeTargetGraph = completeTargetGraph; this.mapping = mapping; this.ged = ged; } public List getListOfEditOperations() { ArrayList listOfEditOperations = new ArrayList<>(); assertTrue(baseEditorialCostForMapping(mapping, completeSourceGraph, completeTargetGraph, listOfEditOperations) == ged); return listOfEditOperations; } } public DiffImpl(PossibleMappingsCalculator possibleMappingsCalculator, SchemaGraph completeSourceGraph, SchemaGraph completeTargetGraph, PossibleMappingsCalculator.PossibleMappings possibleMappings, SchemaDiffingRunningCheck runningCheck) { this.possibleMappingsCalculator = possibleMappingsCalculator; this.completeSourceGraph = completeSourceGraph; this.completeTargetGraph = completeTargetGraph; this.possibleMappings = possibleMappings; this.runningCheck = runningCheck; } OptimalEdit diffImpl(Mapping startMapping, List allSources, List allTargets, AtomicInteger algoIterationCount) throws Exception { int graphSize = allSources.size(); int fixedEditorialCost = baseEditorialCostForMapping(startMapping, completeSourceGraph, completeTargetGraph); int level = startMapping.size(); List allNonFixedTargets = new ArrayList<>(allTargets); startMapping.forEachTarget(allNonFixedTargets::remove); MappingEntry firstMappingEntry = new MappingEntry(startMapping, level, fixedEditorialCost); firstMappingEntry.availableTargetVertices = allNonFixedTargets; OptimalEdit optimalEdit = new OptimalEdit(completeSourceGraph, completeTargetGraph); PriorityQueue queue = new PriorityQueue<>((mappingEntry1, mappingEntry2) -> { int compareResult = Double.compare(mappingEntry1.lowerBoundCost, mappingEntry2.lowerBoundCost); // we prefer higher levels for equal lower bound costs if (compareResult == 0) { return Integer.compare(mappingEntry2.level, mappingEntry1.level); } else { return compareResult; } }); queue.add(firstMappingEntry); while (!queue.isEmpty()) { MappingEntry mappingEntry = queue.poll(); algoIterationCount.incrementAndGet(); if (mappingEntry.lowerBoundCost >= optimalEdit.ged) { // once the lowest lowerBoundCost is not lower than the optimal edit, we are done break; } if (mappingEntry.level > 0 && !mappingEntry.mappingEntriesSiblings.isEmpty()) { addSiblingToQueue( fixedEditorialCost, mappingEntry.level, queue, optimalEdit, allSources, allTargets, mappingEntry); } if (mappingEntry.level < graphSize) { addChildToQueue( fixedEditorialCost, mappingEntry, queue, optimalEdit, allSources, allTargets ); } runningCheck.check(); } return optimalEdit; } // this calculates all children for the provided parentEntry, but only the first is directly added to the queue private void addChildToQueue(int fixedEditorialCost, MappingEntry parentEntry, PriorityQueue queue, OptimalEdit optimalEdit, List allSources, List allTargets ) { Mapping parentPartialMapping = parentEntry.partialMapping; int parentLevel = parentEntry.level; int level = parentLevel + 1; assertTrue(parentLevel == parentPartialMapping.size()); // the available target vertices are the parent queue entry ones plus // minus the additional mapped element in parentPartialMapping ArrayList availableTargetVertices = new ArrayList<>(parentEntry.availableTargetVertices); availableTargetVertices.remove(parentPartialMapping.getTarget(parentLevel - 1)); assertTrue(availableTargetVertices.size() + parentPartialMapping.size() == allTargets.size()); Vertex v_i = allSources.get(parentLevel); // the cost matrix is for the non mapped vertices int costMatrixSize = allSources.size() - parentLevel; // costMatrix gets modified by the hungarian algorithm ... therefore we create two of them double[][] costMatrixForHungarianAlgo = new double[costMatrixSize][costMatrixSize]; double[][] costMatrix = new double[costMatrixSize][costMatrixSize]; Map isolatedVerticesCache = new LinkedHashMap<>(); Map nonFixedParentRestrictions = possibleMappingsCalculator.getNonFixedParentRestrictions(completeSourceGraph, completeTargetGraph, parentPartialMapping); for (int i = parentLevel; i < allSources.size(); i++) { Vertex v = allSources.get(i); int j = 0; for (Vertex u : availableTargetVertices) { double cost = calcLowerBoundMappingCost(v, u, parentPartialMapping, isolatedVerticesCache, nonFixedParentRestrictions); costMatrixForHungarianAlgo[i - parentLevel][j] = cost; costMatrix[i - parentLevel][j] = cost; j++; } runningCheck.check(); } HungarianAlgorithm hungarianAlgorithm = new HungarianAlgorithm(costMatrixForHungarianAlgo); int[] assignments = hungarianAlgorithm.execute(); int editorialCostForMapping = editorialCostForMapping(fixedEditorialCost, parentPartialMapping, completeSourceGraph, completeTargetGraph); double costMatrixSum = getCostMatrixSum(costMatrix, assignments); double lowerBoundForPartialMapping = editorialCostForMapping + costMatrixSum; Mapping newMapping = parentPartialMapping.extendMapping(v_i, availableTargetVertices.get(assignments[0])); if (costMatrixSum >= Integer.MAX_VALUE && optimalEdit.mapping == null) { throw new RuntimeException("bug: could not find any allowed mapping"); } if (lowerBoundForPartialMapping >= optimalEdit.ged) { return; } MappingEntry newMappingEntry = new MappingEntry(newMapping, level, lowerBoundForPartialMapping); LinkedBlockingQueue siblings = new LinkedBlockingQueue<>(); newMappingEntry.mappingEntriesSiblings = siblings; newMappingEntry.assignments = assignments; newMappingEntry.availableTargetVertices = availableTargetVertices; queue.add(newMappingEntry); expandMappingAndUpdateOptimalMapping(fixedEditorialCost, level, optimalEdit, allSources, parentPartialMapping.copy(), assignments, availableTargetVertices, lowerBoundForPartialMapping); calculateRestOfChildren( availableTargetVertices, hungarianAlgorithm, costMatrix, editorialCostForMapping, parentPartialMapping, v_i, optimalEdit.ged, level, siblings ); } private void updateOptimalEdit(OptimalEdit optimalEdit, int newGed, Mapping mapping) { assertTrue(newGed < optimalEdit.ged); optimalEdit.ged = newGed; optimalEdit.mapping = mapping; } // generate all children mappings and save in MappingEntry.sibling private void calculateRestOfChildren(List availableTargetVertices, HungarianAlgorithm hungarianAlgorithm, double[][] costMatrixCopy, double editorialCostForMapping, Mapping partialMapping, Vertex v_i, int upperBound, int level, LinkedBlockingQueue siblings ) { // starting from 1 as we already generated the first one for (int child = 1; child < availableTargetVertices.size(); child++) { int[] assignments = hungarianAlgorithm.nextChild(); if (hungarianAlgorithm.costMatrix[0][assignments[0]] == Integer.MAX_VALUE) { break; } double costMatrixSumSibling = getCostMatrixSum(costMatrixCopy, assignments); double lowerBoundForPartialMappingSibling = editorialCostForMapping + costMatrixSumSibling; Mapping newMappingSibling = partialMapping.extendMapping(v_i, availableTargetVertices.get(assignments[0])); if (lowerBoundForPartialMappingSibling >= upperBound) { break; } MappingEntry sibling = new MappingEntry(newMappingSibling, level, lowerBoundForPartialMappingSibling); sibling.mappingEntriesSiblings = siblings; sibling.assignments = assignments; sibling.availableTargetVertices = availableTargetVertices; siblings.add(sibling); runningCheck.check(); } } // this retrieves the next sibling from MappingEntry.sibling and adds it to the queue if the lowerBound is less than the current upperBound private void addSiblingToQueue( int fixedEditorialCost, int level, PriorityQueue queue, OptimalEdit optimalEdit, List allSources, List allTargets, MappingEntry mappingEntry) throws InterruptedException { assertFalse(mappingEntry.mappingEntriesSiblings.isEmpty()); MappingEntry sibling = mappingEntry.mappingEntriesSiblings.take(); if (sibling.lowerBoundCost < optimalEdit.ged) { queue.add(sibling); // we need to start here from the parent mapping, this is why we remove the last element Mapping toExpand = sibling.partialMapping.copyMappingWithLastElementRemoved(); expandMappingAndUpdateOptimalMapping(fixedEditorialCost, level, optimalEdit, allSources, toExpand, sibling.assignments, sibling.availableTargetVertices, sibling.lowerBoundCost); } } /** * Extend the partial mapping to a full mapping according to the optimal * matching (hungarian algo result) and update the optimal edit if we * found a better one. */ private void expandMappingAndUpdateOptimalMapping(int fixedEditorialCost, int level, OptimalEdit optimalEdit, List allSources, Mapping toExpand, int[] assignments, List availableTargetVertices, double lowerBoundCost) { for (int i = 0; i < assignments.length; i++) { toExpand.add(allSources.get(level - 1 + i), availableTargetVertices.get(assignments[i])); } assertTrue(toExpand.size() == this.completeSourceGraph.size()); int costForFullMapping = editorialCostForMapping(fixedEditorialCost, toExpand, completeSourceGraph, completeTargetGraph); assertTrue(lowerBoundCost <= costForFullMapping); if (costForFullMapping < optimalEdit.ged) { updateOptimalEdit(optimalEdit, costForFullMapping, toExpand); } } private double getCostMatrixSum(double[][] costMatrix, int[] assignments) { double costMatrixSum = 0; for (int i = 0; i < assignments.length; i++) { costMatrixSum += costMatrix[i][assignments[i]]; } return costMatrixSum; } /** * a partial mapping introduces a sub graph. The editorial cost is only calculated with respect to this sub graph. */ /** * lower bound mapping cost between for v -> u in respect to a partial mapping. * It basically tells the minimal costs we can expect for all mappings that come from extending * the partial mapping with v -> u. *

* This is basically the formula (5) from page 6 of https://lijunchang.github.io/pdf/2022-ged-tkde.pdf. *

* * The main difference is that the formula works with undirected graphs, but we have a directed graph, * hence there is no 1/2 factor and for comparing the labels of anchored vertices to v/u we need to * take both directions into account. *

* * The other optimization is that a schema graph will have never a lot of adjacent edges compared to * the overall vertices count, therefore the algorithm for the anchored vertices costs iterates * over the adjacent edges of v/u instead of all the mapped vertices. *

* * Additionally, there is a shortcut for isolated vertices, representing deletion/insertion which is also cached. *

* Some naming: an anchored vertex is a vertex that is mapped via the partial mapping. * An inner edge is an edge between two vertices that are both not anchored (mapped). * The vertices v and u are by definition not mapped. */ private double calcLowerBoundMappingCost(Vertex v, Vertex u, Mapping partialMapping, Map isolatedVerticesCache, Map nonFixedParentRestrictions) { if (nonFixedParentRestrictions.containsKey(v) || partialMapping.hasParentRestriction(v)) { if (!u.isIsolated()) { // Always allow mapping to isolated nodes Vertex uParentRestriction = nonFixedParentRestrictions.get(v); if (uParentRestriction == null) { uParentRestriction = partialMapping.getParentRestriction(v); } Collection parentEdges = completeTargetGraph.getAdjacentEdgesInverseNonCopy(u); if (parentEdges.size() != 1) { return Integer.MAX_VALUE; } Vertex uParent = parentEdges.iterator().next().getFrom(); if (uParent != uParentRestriction) { return Integer.MAX_VALUE; } } } if (!possibleMappings.mappingPossible(v, u)) { return Integer.MAX_VALUE; } if (u.isOfType(SchemaGraph.ISOLATED)) { if (isolatedVerticesCache.containsKey(v)) { return isolatedVerticesCache.get(v); } double result = calcLowerBoundMappingCostForIsolated(v, partialMapping, true); isolatedVerticesCache.put(v, result); return result; } if (v.isOfType(SchemaGraph.ISOLATED)) { if (isolatedVerticesCache.containsKey(u)) { return isolatedVerticesCache.get(u); } double result = calcLowerBoundMappingCostForIsolated(u, partialMapping, false); isolatedVerticesCache.put(u, result); return result; } boolean equalNodes = v.getType().equals(u.getType()) && v.getProperties().equals(u.getProperties()); int anchoredVerticesCost = 0; Multiset multisetInnerEdgeLabelsV = HashMultiset.create(); Multiset multisetInnerEdgeLabelsU = HashMultiset.create(); Collection adjacentEdgesV = completeSourceGraph.getAdjacentEdgesNonCopy(v); Collection adjacentEdgesU = completeTargetGraph.getAdjacentEdgesNonCopy(u); Collection adjacentEdgesInverseV = completeSourceGraph.getAdjacentEdgesInverseNonCopy(v); Collection adjacentEdgesInverseU = completeTargetGraph.getAdjacentEdgesInverseNonCopy(u); Set matchedTargetEdges = new LinkedHashSet<>(); Set matchedTargetEdgesInverse = new LinkedHashSet<>(); for (Edge edgeV : adjacentEdgesV) { Vertex targetTo = partialMapping.getTarget(edgeV.getTo()); if (targetTo == null) { // meaning it is an inner edge(not part of the subgraph induced by the partial mapping) multisetInnerEdgeLabelsV.add(edgeV.getLabel()); continue; } /* question is if the edge from v is mapped onto an edge from u (also edge are not mapped directly, but the vertices are) and if the adjacent edge is mapped onto an adjacent edge, we need to check the labels of the edges */ Edge matchedTargetEdge = completeTargetGraph.getEdge(u, targetTo); if (matchedTargetEdge != null) { matchedTargetEdges.add(matchedTargetEdge); if (!Objects.equals(edgeV.getLabel(), matchedTargetEdge.getLabel())) { anchoredVerticesCost++; } } else { // // no matching adjacent edge from u found means there is no // // edge from edgeV.getTo() to mapped(edgeV.getTo()) // // and we need to increase the costs anchoredVerticesCost++; } } for (Edge edgeV : adjacentEdgesInverseV) { Vertex targetFrom = partialMapping.getTarget(edgeV.getFrom()); // we are only interested in edges from anchored vertices if (targetFrom == null) { continue; } Edge matachedTargetEdge = completeTargetGraph.getEdge(targetFrom, u); if (matachedTargetEdge != null) { matchedTargetEdgesInverse.add(matachedTargetEdge); if (!Objects.equals(edgeV.getLabel(), matachedTargetEdge.getLabel())) { anchoredVerticesCost++; } } else { anchoredVerticesCost++; } } for (Edge edgeU : adjacentEdgesU) { // test if this is an inner edge (meaning it not part of the subgraph induced by the partial mapping) // we know that u is not part of the mapped vertices, therefore we only need to test the "to" vertex if (!partialMapping.containsTarget(edgeU.getTo())) { multisetInnerEdgeLabelsU.add(edgeU.getLabel()); continue; } if (matchedTargetEdges.contains(edgeU)) { continue; } anchoredVerticesCost++; } for (Edge edgeU : adjacentEdgesInverseU) { // we are only interested in edges from anchored vertices if (!partialMapping.containsTarget(edgeU.getFrom()) || matchedTargetEdgesInverse.contains(edgeU)) { continue; } anchoredVerticesCost++; } Multiset intersectionInnerEdgeLabels = Multisets.intersection(multisetInnerEdgeLabelsV, multisetInnerEdgeLabelsU); int multiSetEditDistanceForInnerEdges = Math.max(multisetInnerEdgeLabelsV.size(), multisetInnerEdgeLabelsU.size()) - intersectionInnerEdgeLabels.size(); int result = (equalNodes ? 0 : 1) + multiSetEditDistanceForInnerEdges + anchoredVerticesCost; return result; } /** * Simplified lower bound calc if the source/target vertex is isolated */ private double calcLowerBoundMappingCostForIsolated(Vertex vertex, Mapping partialMapping, boolean sourceOrTarget ) { SchemaGraph schemaGraph = sourceOrTarget ? completeSourceGraph : completeTargetGraph; // every adjacent edge is inserted/deleted for an isolated vertex Collection adjacentEdges = schemaGraph.getAdjacentEdgesNonCopy(vertex); // for the inverse adjacent edges we only count the anchored ones int anchoredInverseEdges = 0; Collection adjacentEdgesInverse = schemaGraph.getAdjacentEdgesInverseNonCopy(vertex); for (Edge edge : adjacentEdgesInverse) { if (partialMapping.contains(edge.getFrom(), sourceOrTarget)) { anchoredInverseEdges++; } } return 1 + adjacentEdges.size() + anchoredInverseEdges; } }





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