The Minimum Degree Algorithm is a heuristic used primarily in graph theory, particularly in relation to graph coloring and ordering. It is most often associated with sparse graphs and aims to minimize the degree of nodes (the number of edges connected to a node) during certain graph operations. Here’s a breakdown of its common applications: ### Applications: 1. **Graph Coloring**: In the context of graph coloring, the Minimum Degree Algorithm is used to color the vertices of a graph.
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At each step choose a remaining vertex of minimum degree in the current elimination graph. This heuristic reduces the size of the immediate Schur complement update and often reduces fill-in, but does not guarantee a globally optimal ordering. Its degrees must reflect earlier fill, rather than just the original graph.