Computing the Treewidth and the Minimum Fill-In with the Modular Decomposition
Using the notion of modular decomposition we extend the class of graphs on which both the treewidth and the minimum fill-in can be solved in polynomial time. We show that if C is a class of graphs that are modularly decomposable into graphs that have a polynomial number of minimal separators, or graphs formed by adding a matching between two cliques, then both the treewidth and the minimum fill-in on C can be solved in polynomial time. For the graphs that are modular decomposable into cycles we give algorithms that use respectively O(n) and O(n3) time for treewidth and minimum fill-in.
KeywordsTreewidth Minimum fill-in Modular decomposition Minimal separators Polynomial algorithms Graph algorithms
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