Greedy Graph Coloring Algorithm
Greedy Graph Coloring computes a coloring of the vertices of a (simple, connected) graph such that no two adjacent +vertices have the same color.
If the graph has different connected components, each component will be treated as a separate simple connected graph.
The algorithm is heuristic and does not guarantee an optimal number of different colors (that is, equal to the chromatic +number of a simple, connected graph).
Colors are represented by the numbers 0, 1, 2,... The greedy algorithm considers the vertices of the graph in sequence +and assigns each vertex its first available color, i.e. the color with the smallest number that is not already used by +one of its neighbors.
The overall worst-case time complexity of the algorithm is O(n^2). In cases where the graph has a fixed degree (a
+constant number of neighbors for each vertex), the time complexity can be approximated as O(n). However, if the graph
+is highly connected (dense) and approaches a complete graph, the time complexity could approach O(n^2).
If no coloring is possible, an empty unordered_map is returned. This is the case when the graph contains no vertices.
Syntax
template <typename GRAPH>
std::unordered_map<vertex_id_t, int> greedy_graph_coloring(const GRAPH& graph);
- graph A graph to perform graph coloring on.
- return An unordered_map where keys are vertex identifiers and values are their respective colors. If no coloring
+is possible, an empty
unordered_mapis returned.