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arXiv · 1402.3473

A subexponential parameterized algorithm for Interval Completion

Ivan Bliznets·Fedor V. Fomin·Marcin Pilipczuk·Michał Pilipczuk
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Abstract

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 algorithm solving this problem. This question was answer affirmatively more than a decade later by Villanger at el. [STOC 2007; SIAM J. Comput. 2009], who presented an algorithm with running time $O(k^{2k}n^3m)$. We give the first subexponential parameterized algorithm solving Interval Completion in time $k^{O(\sqrt{k})} n^{O(1)}$. This adds Interval Completion to a very small list of parameterized graph modification problems solvable in subexponential time.

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Ivan Bliznets, Fedor V. Fomin, Marcin Pilipczuk, Michał Pilipczuk. 2014-02-13. A subexponential parameterized algorithm for Interval Completion. https://arxiv.org/abs/1402.3473

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