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A 42k Kernel for the Complementary Maximal Strip Recovery Problem

  • Wenjun Li
  • Haiyan Liu
  • Jianxin WangEmail author
  • Lingyun Xiang
  • Yongjie Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

In the Complementary Maximal Strip Recovery problem (CMSR), we are given two strings \(S_1\) and \(S_2\) of distinct letters, where each letter appears either in the positive form or the negative form. The question is whether there are k letters whose deletion results in two matched strings. String \(S_1\) matches string \(S_2\) if there are partitions of \(S_1\) and \(S_2\), such that, for each component \(S_1^i\) of the partition of \(S_1\), there is a unique component \(S_2^j\) in the partition of \(S_2\) which is either equal to \(S_1^i\) or can be obtained from \(S_1^i\) by firstly reversing the order of the letters and then negating the letters. The CMSR problem is known to be NP-hard and fixed-parameter tractable with respect to k. In particular, a linear kernel of size \(74k+4\) was developed based on 8 reduction rules. Very recently, by imposing 3 new reduction rules to the previous kernelization, the linear kernel was improved to 58k. We aim to simplify the kernelization, yet obtain an improved kernel. In particular, we study 7 reduction rules which lead to a linear kernel of size \({42k+24}\).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Wenjun Li
    • 1
  • Haiyan Liu
    • 1
  • Jianxin Wang
    • 2
    Email author
  • Lingyun Xiang
    • 1
  • Yongjie Yang
    • 2
  1. 1.Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on TransportationChangsha University of Science and TechnologyChangshaChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina

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