ceres-solver/internal/ceres/graph_algorithms_test.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2023 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "ceres/graph_algorithms.h"

#include <algorithm>
#include <memory>
#include <vector>

#include "absl/container/flat_hash_set.h"
#include "ceres/graph.h"
#include "ceres/internal/export.h"
#include "gtest/gtest.h"

namespace ceres::internal {

TEST(IndependentSetOrdering, Chain) {
  Graph<int> graph;
  graph.AddVertex(0);
  graph.AddVertex(1);
  graph.AddVertex(2);
  graph.AddVertex(3);
  graph.AddVertex(4);

  graph.AddEdge(0, 1);
  graph.AddEdge(1, 2);
  graph.AddEdge(2, 3);
  graph.AddEdge(3, 4);

  // 0-1-2-3-4
  // 0, 2, 4 should be in the independent set.
  std::vector<int> ordering;
  int independent_set_size = IndependentSetOrdering(graph, &ordering);

  sort(ordering.begin(), ordering.begin() + 3);
  sort(ordering.begin() + 3, ordering.end());

  EXPECT_EQ(independent_set_size, 3);
  EXPECT_EQ(ordering.size(), 5);
  EXPECT_EQ(ordering[0], 0);
  EXPECT_EQ(ordering[1], 2);
  EXPECT_EQ(ordering[2], 4);
  EXPECT_EQ(ordering[3], 1);
  EXPECT_EQ(ordering[4], 3);
}

TEST(IndependentSetOrdering, Star) {
  Graph<int> graph;
  graph.AddVertex(0);
  graph.AddVertex(1);
  graph.AddVertex(2);
  graph.AddVertex(3);
  graph.AddVertex(4);

  graph.AddEdge(0, 1);
  graph.AddEdge(0, 2);
  graph.AddEdge(0, 3);
  graph.AddEdge(0, 4);

  //      1
  //      |
  //    4-0-2
  //      |
  //      3
  // 1, 2, 3, 4 should be in the independent set.
  std::vector<int> ordering;
  int independent_set_size = IndependentSetOrdering(graph, &ordering);
  EXPECT_EQ(independent_set_size, 4);
  EXPECT_EQ(ordering.size(), 5);
  EXPECT_EQ(ordering[4], 0);
  sort(ordering.begin(), ordering.begin() + 4);
  EXPECT_EQ(ordering[0], 1);
  EXPECT_EQ(ordering[1], 2);
  EXPECT_EQ(ordering[2], 3);
  EXPECT_EQ(ordering[3], 4);
}

TEST(Degree2MaximumSpanningForest, PreserveWeights) {
  WeightedGraph<int> graph;
  graph.AddVertex(0, 1.0);
  graph.AddVertex(1, 2.0);
  graph.AddEdge(0, 1, 0.5);
  graph.AddEdge(1, 0, 0.5);

  std::unique_ptr<WeightedGraph<int>> forest(
      Degree2MaximumSpanningForest(graph));

  const absl::flat_hash_set<int>& vertices = forest->vertices();
  EXPECT_EQ(vertices.size(), 2);
  EXPECT_EQ(forest->VertexWeight(0), 1.0);
  EXPECT_EQ(forest->VertexWeight(1), 2.0);
  EXPECT_EQ(forest->Neighbors(0).size(), 1.0);
  EXPECT_EQ(forest->EdgeWeight(0, 1), 0.5);
}

TEST(Degree2MaximumSpanningForest, StarGraph) {
  WeightedGraph<int> graph;
  graph.AddVertex(0);
  graph.AddVertex(1);
  graph.AddVertex(2);
  graph.AddVertex(3);
  graph.AddVertex(4);

  graph.AddEdge(0, 1, 1.0);
  graph.AddEdge(0, 2, 2.0);
  graph.AddEdge(0, 3, 3.0);
  graph.AddEdge(0, 4, 4.0);

  std::unique_ptr<WeightedGraph<int>> forest(
      Degree2MaximumSpanningForest(graph));
  const absl::flat_hash_set<int>& vertices = forest->vertices();
  EXPECT_EQ(vertices.size(), 5);

  {
    const absl::flat_hash_set<int>& neighbors = forest->Neighbors(0);
    EXPECT_EQ(neighbors.size(), 2);
    EXPECT_TRUE(neighbors.find(4) != neighbors.end());
    EXPECT_TRUE(neighbors.find(3) != neighbors.end());
  }

  {
    const absl::flat_hash_set<int>& neighbors = forest->Neighbors(3);
    EXPECT_EQ(neighbors.size(), 1);
    EXPECT_TRUE(neighbors.find(0) != neighbors.end());
  }

  {
    const absl::flat_hash_set<int>& neighbors = forest->Neighbors(4);
    EXPECT_EQ(neighbors.size(), 1);
    EXPECT_TRUE(neighbors.find(0) != neighbors.end());
  }

  {
    const absl::flat_hash_set<int>& neighbors = forest->Neighbors(1);
    EXPECT_EQ(neighbors.size(), 0);
  }

  {
    const absl::flat_hash_set<int>& neighbors = forest->Neighbors(2);
    EXPECT_EQ(neighbors.size(), 0);
  }
}

TEST(VertexTotalOrdering, TotalOrdering) {
  Graph<int> graph;
  graph.AddVertex(0);
  graph.AddVertex(1);
  graph.AddVertex(2);
  graph.AddVertex(3);

  // 0-1
  //   |
  // 2-3
  // 0,1 and 2 have degree 1 and 3 has degree 2.
  graph.AddEdge(0, 1);
  graph.AddEdge(2, 3);
  VertexTotalOrdering<int> less_than(graph);

  for (int i = 0; i < 4; ++i) {
    EXPECT_FALSE(less_than(i, i)) << "Failing vertex: " << i;
    for (int j = 0; j < 4; ++j) {
      if (i != j) {
        EXPECT_TRUE(less_than(i, j) ^ less_than(j, i))
            << "Failing vertex pair: " << i << " " << j;
      }
    }
  }

  for (int i = 0; i < 3; ++i) {
    EXPECT_TRUE(less_than(i, 3));
    EXPECT_FALSE(less_than(3, i));
  }
}

TEST(StableIndependentSet, BreakTies) {
  Graph<int> graph;
  graph.AddVertex(0);
  graph.AddVertex(1);
  graph.AddVertex(2);
  graph.AddVertex(3);

  graph.AddEdge(0, 1);
  graph.AddEdge(0, 2);
  graph.AddEdge(0, 3);
  graph.AddEdge(1, 2);
  graph.AddEdge(1, 3);
  graph.AddEdge(2, 3);

  // Since this is a completely connected graph, the independent set
  // contains exactly one vertex. StableIndependentSetOrdering
  // guarantees that it will always be the first vertex in the
  // ordering vector.
  {
    std::vector<int> ordering;
    ordering.push_back(0);
    ordering.push_back(1);
    ordering.push_back(2);
    ordering.push_back(3);
    const int independent_set_size =
        StableIndependentSetOrdering(graph, &ordering);
    EXPECT_EQ(independent_set_size, 1);
    EXPECT_EQ(ordering[0], 0);
  }

  {
    std::vector<int> ordering;
    ordering.push_back(1);
    ordering.push_back(0);
    ordering.push_back(2);
    ordering.push_back(3);
    const int independent_set_size =
        StableIndependentSetOrdering(graph, &ordering);
    EXPECT_EQ(independent_set_size, 1);
    EXPECT_EQ(ordering[0], 1);
  }
}

}  // namespace ceres::internal