Subexponential Parameterized Algorithm for Minimum Fill-In

Subexponential parameterized algorithm for minimum fill-in

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) + knm) 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(2O( √ k log k) + knm). ...

A subexponential parameterized algorithm for Interval Completion

In the Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into an interval graph, i.e., a graph admitting an intersection model of intervals on a line. Motivated by applications in sparse matrix multiplication and molecular biology, Kaplan, Shamir and Tarjan [FOCS 1994; SIAM J. Comput. 1999] asked for a fixed-parameter a...

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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 timeO(2O(k)+k2nm) on graphs with n vertices and m edges and thus is fixed parameter tractable. Here, we give the first subexponential parameterized algorithm solving Minimum Fill-in in time O(2O( √ k log +knm). This ...

A subexponential parameterized algorithm for Subset TSP on planar graphs

A Subexponential Parameterized Algorithm for Proper Interval Completion

In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length intervals on a line. The study of Proper Interval Completion from the viewpoint of parameterized complexity has been initiated by Kaplan, Shamir and Tarjan [FOCS 199...