Welsh powell coloring

include/CXXGraph/Graph/Algorithm/welshPowellColoring_impl.hpp

@@ -0,0 +1,58 @@
+//
+// Created by jjsm on 1/22/24.
+//
+
+#ifndef CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__
+#define CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__
+
+#pragma once
+
+#include "CXXGraph/Graph/Graph_decl.h"
+
+namespace CXXGraph {
+template <typename T>
+std::map<Node<T>, int> Graph<T>::welshPowellColoring() const {
+  auto adjMatrix = *getAdjMatrix();
+  std::unordered_map<std::shared_ptr<const Node<T>>, int> degreeOfVertexMap = {};
+
+  // Find the degree of each vertex and put them in a map
+  for (auto &[nodeFrom, nodeToEdgeVec] : adjMatrix) {
+    degreeOfVertexMap[nodeFrom] = nodeToEdgeVec.size();
+  }
+
+  // Transform the map to the vector to sort
+  std::vector<std::pair<std::shared_ptr<const Node<T>>, int>> degreeOfVertexVector(degreeOfVertexMap.begin(), degreeOfVertexMap.end());
+
+  // Sort them based on the vertex degree
+  std::sort(degreeOfVertexVector.begin(), degreeOfVertexVector.end(), [](const auto& left, const auto& right) {
+    return left.second > right.second;
+  });
+
+  // Create a new map of coloring, where the keys are the nodes, and the value is the color order (assigned by integer)
+  std::map<Node<T>, int> mapOfColoring;
+  for (auto &[nodeFrom, _] : adjMatrix) {
+    mapOfColoring[*nodeFrom] = 0;
+  }
+
+  // Going down the list of vertex based on degrees
+  for (const auto& [node, _] : degreeOfVertexVector) {
+    // Find the smallest unused color for the current vertex
+    std::vector<int> usedColors(degreeOfVertexVector.size() + 1, 0);
+
+    for (const auto &[neighbor, _] : adjMatrix[node]) {
+      usedColors[mapOfColoring[*neighbor]] = 1;
+    }
+
+    // Assign the smallest unused color to the current vertex
+    for (int c = 1; c < usedColors.size(); c++) {
+      if (usedColors[c] == 0) {
+        mapOfColoring[*node] = c;
+        break;
+      }
+    }
+  }
+
+  return mapOfColoring;
+}
+}
+#endif  // CXXGRAPH_WELSHPOWELLCOLORING_IMPL_H__

include/CXXGraph/Graph/Graph.h

@@ -41,6 +41,7 @@
 #include "CXXGraph/Graph/Algorithm/Tarjan_impl.hpp"
 #include "CXXGraph/Graph/Algorithm/TopologicalSort_impl.hpp"
 #include "CXXGraph/Graph/Algorithm/TransitiveReduction_impl.hpp"
+#include "CXXGraph/Graph/Algorithm/welshPowellColoring_impl.hpp"
 
 // IO Operation
 #include "CXXGraph/Graph/IO/IOUtility_impl.hpp"

include/CXXGraph/Graph/Graph_decl.h

@@ -795,6 +795,17 @@ class Graph {
   virtual double fordFulkersonMaxFlow(const Node<T> &source,
                                       const Node<T> &target) const;
 
+  /**
+    * @brief Welsh-Powell Coloring algorithm
+    * @return a std::map of keys being the nodes and the values being the color
+    * order (by integer) starting from 1.
+    * Source :
+    *          https://www.youtube.com/watch?v=SLkyDuG1Puw&ab_channel=TheLogicalLearning
+    *          https://www.geeksforgeeks.org/welsh-powell-graph-colouring-algorithm/
+    *          https://www.tutorialspoint.com/de-powell-graph-colouring-algorithm
+   */
+  virtual std::map<Node<T>, int> welshPowellColoring()  const;
+
   /**
    * \brief
    * This function writes the graph to an output file

test/CMakeLists.txt

@@ -98,4 +98,5 @@ if(TEST)
     add_test(test_transitive_reductiono test_exe --gtest_filter=TransitiveReduction*)
     add_test(test_union_find test_exe --gtest_filter=UnionFind*)
     add_test(test_floyd_warshall test_exe --gtest_filter=FloydWarshall*)
+    add_test(test_welsh_powell_coloring test_exe --gtest_filter=welshPowellColoring*)
 endif(TEST)

test/welshPowellColoringTest.cpp

@@ -0,0 +1,174 @@
+#include "CXXGraph/CXXGraph.hpp"
+#include "gtest/gtest.h"
+
+TEST(welshPowellColoring, one_edge_two_nodes_undirected) {
+  CXXGraph::Node<int> node1("1", 1);
+  CXXGraph::Node<int> node2("2", 2);
+
+  CXXGraph::UndirectedWeightedEdge<int> edge12(3, node1, node2,4);
+
+  CXXGraph::T_EdgeSet<int> edgeSet;
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedWeightedEdge<int>>(edge12));
+
+  CXXGraph::Graph<int> graph(edgeSet);
+
+  auto result = graph.welshPowellColoring();
+
+  // get the highest coloring order
+  auto highest_coloring_order = std::max_element(result.begin(), result.end(),
+                                     [](const auto& lhs, const auto& rhs) {
+                                       return lhs.second < rhs.second;
+                                     }
+  )->second;
+  ASSERT_EQ(graph.isUndirectedGraph(), true);
+
+  // Asserts that the chromatic color of the graph is 2
+  ASSERT_EQ(highest_coloring_order, 2);
+}
+
+TEST(welshPowellColoring, undirected_simon_james) {
+  // https://www.youtube.com/watch?v=CQIW2mLfG04&ab_channel=SimonJames
+  CXXGraph::Node<int> nodeA("a", 1);
+  CXXGraph::Node<int> nodeB("b", 1);
+  CXXGraph::Node<int> nodeC("c", 1);
+  CXXGraph::Node<int> nodeD("d", 1);
+  CXXGraph::Node<int> nodeE("e", 1);
+  CXXGraph::Node<int> nodeF("f", 1);
+  CXXGraph::Node<int> nodeG("g", 1);
+  CXXGraph::Node<int> nodeH("h", 1);
+  CXXGraph::Node<int> nodeI("i", 1);
+  CXXGraph::Node<int> nodeJ("j", 1);
+  CXXGraph::Node<int> nodeK("k", 1);
+
+
+  CXXGraph::UndirectedEdge<int> edgeAB(1, nodeA, nodeB),
+      edgeBA(1, nodeB, nodeA), //
+
+      edgeAC(1, nodeA, nodeC),
+      edgeCA(1, nodeC, nodeA), //
+
+      edgeAD(1, nodeA, nodeD),
+      edgeDA(1, nodeD, nodeA), //
+
+      edgeAK(1, nodeA, nodeK),
+      edgeKA(1, nodeK, nodeA),
+
+      edgeAH(1, nodeA, nodeH),
+      edgeHA(1, nodeA, nodeH), //
+
+      edgeAE(1, nodeA, nodeE),
+      edgeEA(1, nodeA, nodeH), //
+
+      edgeAG(1, nodeA, nodeG),
+      edgeGA(1, nodeA, nodeG), //
+
+      edgeBK(1, nodeB, nodeK),
+      edgeKB(1, nodeK, nodeB), //
+
+      edgeBI(1, nodeB, nodeI),
+      edgeIB(1, nodeI, nodeB), //
+
+      edgeBJ(1, nodeB, nodeJ),
+      edgeJB(1, nodeJ, nodeB),
+
+      edgeBF(1, nodeB, nodeF),
+      edgeFB(1, nodeF, nodeB), //
+
+      edgeBD(1, nodeB, nodeD),
+      edgeDB(1, nodeD, nodeB), //
+
+      edgeCE(1, nodeC, nodeE),
+      edgeEC(1, nodeE, nodeC), //
+
+      edgeCD(1, nodeC, nodeD),
+      edgeDC(1, nodeD, nodeC), //
+
+      edgeCH(1, nodeC, nodeH),
+      edgeHC(1, nodeH, nodeC), //
+
+      edgeCG(1, nodeC, nodeG),
+      edgeGC(1, nodeG, nodeC), //
+
+      edgeDE(1, nodeD, nodeE),
+      edgeED(1, nodeD, nodeE), //
+
+      edgeEK(1, nodeE, nodeK),
+      edgeKE(1, nodeK, nodeE), //
+
+      edgeFI(1, nodeF, nodeI),
+      edgeIF(1, nodeI, nodeF),
+
+      edgeFJ(1, nodeF, nodeJ),
+      edgeJF(1, nodeJ, nodeF),
+
+      edgeFG(1, nodeF, nodeG),
+      edgeGF(1, nodeG, nodeF),
+
+      edgeGH(1, nodeG, nodeH),
+      edgeHG(1, nodeH, nodeG),
+
+      edgeIJ(1, nodeI, nodeJ), //
+      edgeJI(1, nodeJ, nodeI); //
+
+  CXXGraph::T_EdgeSet<int> edgeSet;
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAB));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAC));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAD));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAK));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAH));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAE));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeAG));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBK));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBI));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBJ));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBF));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeBD));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCE));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCD));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCH));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeCG));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeDE));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeEK));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFI));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFJ));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeFG));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeGH));
+
+  edgeSet.insert(std::make_shared<CXXGraph::UndirectedEdge<int>>(edgeIJ));
+
+
+  CXXGraph::Graph<int> graph(edgeSet);
+
+  auto result = graph.welshPowellColoring();
+  auto highest_coloring_order = std::max_element(result.begin(), result.end(),
+                                                 [](const auto& lhs, const auto& rhs) {
+                                                   return lhs.second < rhs.second;
+                                                 }
+  )->second;
+
+  ASSERT_EQ(graph.isUndirectedGraph(), true);
+  // Asserts that the chromatic color of the graph is 4, as indicated in 2:30 of video
+  ASSERT_EQ(highest_coloring_order, 4);
+}