Abstract
The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. Kaplan, Shamir, and Tarjan [FOCS 1994] have shown that the problem is solvable in time O(2O(k) + k2nm) on graphs with n vertices and m edges and thus is fixed parameter tractable. Here, we give the first subexponential parameterizedv algorithm solving Minimum Fill-in in time [EQUATION]. This substantially lowers the complexity of the problem. Techniques developed for Minimum Fill-in can be used to obtain subexponential parameterized algorithms for several related problems including Minimum Chain Completion, Chordal Graph Sandwich, and Triangulating Colored Graph.
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