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Subexponential Parameterized Algorithm for Minimum Fill-In
SIAM journal on computing (Print)
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(2 O(k) + k 2 nm) on graphs with n vertices and m edges and thus is fixed parameter tractable. Here, we give the first subexponential parameterized algorithm solving Minimum Fillin in time O(2 O( √ k log k) + k 2 nm). This substantially lowers the complexity of the problem. Techniques developed for Minimumdoi:10.1137/11085390x fatcat:eufcxsb7p5gvjbklcetvnvldhe