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Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping

Authors Christian Komusiewicz, Mateus de Oliveira Oliveira, Meirav Zehavi

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Christian Komusiewicz
Mateus de Oliveira Oliveira
Meirav Zehavi

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Christian Komusiewicz, Mateus de Oliveira Oliveira, and Meirav Zehavi. Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CPM.2017.11

Abstract

In the Maximum-Duo Preservation String Mapping (Max-Duo PSM) problem, the input consists of two related strings A and B of length n and a nonnegative integer k. The objective is to determine whether there exists a mapping m from the set of positions of A to the set of positions of B that maps only to positions with the same character and preserves at least k duos, which are pairs of adjacent positions. We develop a randomized algorithm that solves Max-Duo PSM in time 4^k * n^{O(1)}, and a deterministic algorithm that solves this problem in time 6.855^k * n^{O(1)}. The previous best known (deterministic) algorithm for this problem has running time (8e)^{2k+o(k)} * n^{O(1)} [Beretta et al., Theor. Comput. Sci. 2016]. We also show that Max-Duo PSM admits a problem kernel of size O(k^3), improving upon the previous best known problem kernel of size O(k^6).

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Keywords
  • comparative genomics
  • parameterized complexity
  • kernelization

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