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A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem

Authors Haitao Jiang, Jiong Guo, Daming Zhu, Binhai Zhu



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Author Details

Haitao Jiang
  • Department of Computer Science and Technology, Shandong University, China
Jiong Guo
  • Department of Computer Science and Technology, Shandong University, China
Daming Zhu
  • Department of Computer Science and Technology, Shandong University, China
Binhai Zhu
  • Gianforte School of Computing, Montana State University, Bozeman, MT 59717, USA

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Haitao Jiang, Jiong Guo, Daming Zhu, and Binhai Zhu. A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 5:1-5:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.CPM.2019.5

Abstract

The Maximal Strip Recovery problem (MSR) and its complementary (CMSR) are well-studied NP-hard problems in computational genomics. The input of these dual problems are two signed permutations. The goal is to delete some gene markers from both permutations, such that, in the remaining permutations, each gene marker has at least one common neighbor. Equivalently, the resulting permutations could be partitioned into common strips of length at least two. Then MSR is to maximize the number of remaining genes, while the objective of CMSR is to delete the minimum number of gene markers. In this paper, we present a new approximation algorithm for the Complementary Maximal Strip Recovery (CMSR) problem. Our approximation factor is 2, improving the currently best 7/3-approximation algorithm. Although the improvement on the factor is not huge, the analysis is greatly simplified by a compensating method, commonly referred to as the non-oblivious local search technique. In such a method a substitution may not always increase the value of the current solution (it sometimes may even decrease the solution value), though it always improves the value of another function seemingly unrelated to the objective function.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Maximal strip recovery
  • complementary maximal strip recovery
  • computational genomics
  • approximation algorithm
  • local search

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References

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