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arXiv · 1402.3472

A subexponential parameterized algorithm for Proper Interval Completion

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

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 1994; SIAM J. Comput. 1999], who showed an algorithm for the problem working in $O(16^k (n + m))$ time. In this paper we present an algorithm with running time $k^{O(k^{2/3})} + O(nm(kn + m))$, which is the first subexponential parameterized algorithm for Proper Interval Completion.

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Ivan Bliznets, Fedor V. Fomin, Marcin Pilipczuk, Michał Pilipczuk. 2014-02-13. A subexponential parameterized algorithm for Proper Interval Completion. https://arxiv.org/abs/1402.3472

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