Exemplo n.º 1
0
        /// <summary>
        /// Colors graph vertices greedily processing them in order of <paramref name="verticesOrdered"/>.
        /// </summary>
        /// <param name="graph">Graph to be colored.</param>
        /// <param name="verticesOrdered">Ordering of graph vertices to use in algorithm.</param>
        /// <param name="adjacency"><paramref name="graph"/> adjacency to save calculations
        /// when doing multiple colorings.</param>
        /// <returns>Vertex coloring of provided graph.</returns>
        public static GraphColoring ColorGreedilyWithVertexOrder(this Graph graph, IEnumerable <Vertex> verticesOrdered,
                                                                 VertexAdjacency adjacency)
        {
            var maxDegree = adjacency.AdjacentVertices.Max(p => p.Value.Count);
            var colors    = Enumerable.Range(1, maxDegree + 2);
            var coloring  = new MutableGraphColoring(graph);

            foreach (var vertex in verticesOrdered)
            {
                var adjacentVertices = adjacency.AdjacentVertices[vertex];
                var usedColors       = adjacentVertices.Select(v => coloring[v]).Where(c => c != null).Select(c => c.Value);
                var color            = colors.Except(usedColors).First();
                coloring[vertex] = color;
            }
            return(coloring.ToImmutable());
        }
Exemplo n.º 2
0
        /// <summary>
        /// Colors graph using G.I.S (Greedy Independent Sets) algorithm. See remarks in <see cref="ColorGreedyIndependentSets(Graph)"/>.
        /// </summary>
        /// <param name="graph">Graph to be colored.</param>
        /// <param name="adjacency"><paramref name="graph"/> adjacency to save calculations
        /// when doing multiple colorings.</param>
        /// <returns>Vertex coloring of provided graph.</returns>
        public static GraphColoring ColorGreedyIndependentSets(this Graph graph, VertexAdjacency adjacency)
        {
            var maxDegree = adjacency.AdjacentVertices.Max(p => p.Value.Count);
            var color     = 1;
            var coloring  = new MutableGraphColoring(graph);

            while (coloring.VertexColors.Count < graph.Vertices.Count)
            {
                var induced          = adjacency.InducedSubgraphByRemovingVertices(coloring.VertexColors.Keys);
                var inducedAdjacency = induced.Adjacency();
                while (induced.Subgraph.Vertices.Count > 0)
                {
                    var vertex = induced.Subgraph.MinDegreeVertex(inducedAdjacency.VertexDegrees());
                    coloring[vertex] = color;
                    induced          = inducedAdjacency.InducedSubgraphByRemovingVertices(inducedAdjacency.AdjacentVertices[vertex].Add(vertex));
                    inducedAdjacency = induced.Adjacency();
                }
                color++;
            }
            return(coloring.ToImmutable());
        }