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Welsh powell coloring (#391)
* Wokring on getNodeSet, breaking tests * Added welshPowellColoring algorithm, breaking 1 test in welshPowerColoringTest.cpp * Removing assertions and <cassert> * Transitioned from shared_ptr to node<T>, all tests passed * Beautify code and fix comments in code * Sync from fork
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‎include/CXXGraph/Graph/Algorithm/welshPowellColoring_impl.hpp

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//
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// Created by jjsm on 1/22/24.
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//
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#ifndef CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__
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#define CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__
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#pragma once
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#include "CXXGraph/Graph/Graph_decl.h"
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namespace CXXGraph {
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template <typename T>
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std::map<Node<T>, int> Graph<T>::welshPowellColoring() const {
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auto adjMatrix = *getAdjMatrix();
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std::unordered_map<std::shared_ptr<const Node<T>>, int> degreeOfVertexMap = {};
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// Find the degree of each vertex and put them in a map
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for (auto &[nodeFrom, nodeToEdgeVec] : adjMatrix) {
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degreeOfVertexMap[nodeFrom] = nodeToEdgeVec.size();
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}
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// Transform the map to the vector to sort
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std::vector<std::pair<std::shared_ptr<const Node<T>>, int>> degreeOfVertexVector(degreeOfVertexMap.begin(), degreeOfVertexMap.end());
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// Sort them based on the vertex degree
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std::sort(degreeOfVertexVector.begin(), degreeOfVertexVector.end(), [](const auto& left, const auto& right) {
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return left.second > right.second;
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});
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// Create a new map of coloring, where the keys are the nodes, and the value is the color order (assigned by integer)
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std::map<Node<T>, int> mapOfColoring;
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for (auto &[nodeFrom, _] : adjMatrix) {
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mapOfColoring[*nodeFrom] = 0;
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}
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// Going down the list of vertex based on degrees
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for (const auto& [node, _] : degreeOfVertexVector) {
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// Find the smallest unused color for the current vertex
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std::vector<int> usedColors(degreeOfVertexVector.size() + 1, 0);
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for (const auto &[neighbor, _] : adjMatrix[node]) {
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usedColors[mapOfColoring[*neighbor]] = 1;
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}
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// Assign the smallest unused color to the current vertex
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for (int c = 1; c < usedColors.size(); c++) {
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if (usedColors[c] == 0) {
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mapOfColoring[*node] = c;
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break;
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}
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}
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}
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return mapOfColoring;
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}
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}
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#endif // CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__

‎include/CXXGraph/Graph/Graph.h

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#include "CXXGraph/Graph/Algorithm/Tarjan_impl.hpp"
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#include "CXXGraph/Graph/Algorithm/TopologicalSort_impl.hpp"
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#include "CXXGraph/Graph/Algorithm/TransitiveReduction_impl.hpp"
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#include "CXXGraph/Graph/Algorithm/welshPowellColoring_impl.hpp"
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// IO Operation
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#include "CXXGraph/Graph/IO/IOUtility_impl.hpp"

‎include/CXXGraph/Graph/Graph_decl.h

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virtual double fordFulkersonMaxFlow(const Node<T> &source,
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const Node<T> &target) const;
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/**
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* @brief Welsh-Powell Coloring algorithm
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* @return a std::map of keys being the nodes and the values being the color
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* order (by integer) starting from 1.
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* Source :
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* https://www.youtube.com/watch?v=SLkyDuG1Puw&ab_channel=TheLogicalLearning
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* https://www.geeksforgeeks.org/welsh-powell-graph-colouring-algorithm/
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* https://www.tutorialspoint.com/de-powell-graph-colouring-algorithm
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*/
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virtual std::map<Node<T>, int> welshPowellColoring() const;
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/**
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* \brief
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* This function writes the graph to an output file

‎test/CMakeLists.txt

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add_test(test_transitive_reductiono test_exe --gtest_filter=TransitiveReduction*)
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add_test(test_union_find test_exe --gtest_filter=UnionFind*)
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add_test(test_floyd_warshall test_exe --gtest_filter=FloydWarshall*)
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add_test(test_welsh_powell_coloring test_exe --gtest_filter=welshPowellColoring*)
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endif(TEST)

‎test/welshPowellColoringTest.cpp

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#include "CXXGraph/CXXGraph.hpp"
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#include "gtest/gtest.h"
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TEST(welshPowellColoring, one_edge_two_nodes_undirected) {
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CXXGraph::Node<int> node1("1", 1);
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CXXGraph::Node<int> node2("2", 2);
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CXXGraph::UndirectedWeightedEdge<int> edge12(3, node1, node2,4);
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CXXGraph::T_EdgeSet<int> edgeSet;
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedWeightedEdge<int>>(edge12));
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CXXGraph::Graph<int> graph(edgeSet);
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auto result = graph.welshPowellColoring();
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// get the highest coloring order
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auto highest_coloring_order = std::max_element(result.begin(), result.end(),
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[](const auto& lhs, const auto& rhs) {
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return lhs.second < rhs.second;
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}
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)->second;
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ASSERT_EQ(graph.isUndirectedGraph(), true);
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// Asserts that the chromatic color of the graph is 2
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ASSERT_EQ(highest_coloring_order, 2);
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}
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TEST(welshPowellColoring, undirected_simon_james) {
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// https://www.youtube.com/watch?v=CQIW2mLfG04&ab_channel=SimonJames
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CXXGraph::Node<int> nodeA("a", 1);
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CXXGraph::Node<int> nodeB("b", 1);
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CXXGraph::Node<int> nodeC("c", 1);
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CXXGraph::Node<int> nodeD("d", 1);
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CXXGraph::Node<int> nodeE("e", 1);
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CXXGraph::Node<int> nodeF("f", 1);
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CXXGraph::Node<int> nodeG("g", 1);
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CXXGraph::Node<int> nodeH("h", 1);
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CXXGraph::Node<int> nodeI("i", 1);
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CXXGraph::Node<int> nodeJ("j", 1);
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CXXGraph::Node<int> nodeK("k", 1);
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CXXGraph::UndirectedEdge<int> edgeAB(1, nodeA, nodeB),
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edgeBA(1, nodeB, nodeA), //
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edgeAC(1, nodeA, nodeC),
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edgeCA(1, nodeC, nodeA), //
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edgeAD(1, nodeA, nodeD),
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edgeDA(1, nodeD, nodeA), //
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edgeAK(1, nodeA, nodeK),
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edgeKA(1, nodeK, nodeA),
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edgeAH(1, nodeA, nodeH),
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edgeHA(1, nodeA, nodeH), //
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edgeAE(1, nodeA, nodeE),
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edgeEA(1, nodeA, nodeH), //
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edgeAG(1, nodeA, nodeG),
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edgeGA(1, nodeA, nodeG), //
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edgeBK(1, nodeB, nodeK),
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edgeKB(1, nodeK, nodeB), //
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edgeBI(1, nodeB, nodeI),
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edgeIB(1, nodeI, nodeB), //
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edgeBJ(1, nodeB, nodeJ),
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edgeJB(1, nodeJ, nodeB),
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edgeBF(1, nodeB, nodeF),
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edgeFB(1, nodeF, nodeB), //
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edgeBD(1, nodeB, nodeD),
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edgeDB(1, nodeD, nodeB), //
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edgeCE(1, nodeC, nodeE),
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edgeEC(1, nodeE, nodeC), //
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edgeCD(1, nodeC, nodeD),
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edgeDC(1, nodeD, nodeC), //
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edgeCH(1, nodeC, nodeH),
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edgeHC(1, nodeH, nodeC), //
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edgeCG(1, nodeC, nodeG),
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edgeGC(1, nodeG, nodeC), //
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edgeDE(1, nodeD, nodeE),
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edgeED(1, nodeD, nodeE), //
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edgeEK(1, nodeE, nodeK),
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edgeKE(1, nodeK, nodeE), //
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edgeFI(1, nodeF, nodeI),
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edgeIF(1, nodeI, nodeF),
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edgeFJ(1, nodeF, nodeJ),
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edgeJF(1, nodeJ, nodeF),
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edgeFG(1, nodeF, nodeG),
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edgeGF(1, nodeG, nodeF),
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edgeGH(1, nodeG, nodeH),
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edgeHG(1, nodeH, nodeG),
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edgeIJ(1, nodeI, nodeJ), //
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edgeJI(1, nodeJ, nodeI); //
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CXXGraph::T_EdgeSet<int> edgeSet;
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAB));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAC));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAD));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAK));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAH));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAE));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAG));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBK));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBI));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBJ));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBF));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBD));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCE));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCD));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCH));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCG));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeDE));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeEK));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFI));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFJ));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFG));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeGH));
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edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeIJ));
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CXXGraph::Graph<int> graph(edgeSet);
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auto result = graph.welshPowellColoring();
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auto highest_coloring_order = std::max_element(result.begin(), result.end(),
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[](const auto& lhs, const auto& rhs) {
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return lhs.second < rhs.second;
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}
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)->second;
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ASSERT_EQ(graph.isUndirectedGraph(), true);
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// Asserts that the chromatic color of the graph is 4, as indicated in 2:30 of video
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ASSERT_EQ(highest_coloring_order, 4);
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}

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