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Faster STR-EC-LCS Computation

  • Kohei YamadaEmail author
  • Yuto Nakashima
  • Shunsuke Inenaga
  • Hideo Bannai
  • Masayuki Takeda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)

Abstract

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings A and B. More recently, a set of four constrained LCS problems (called generalized constrained LCS problem) were proposed by Chen and Chao [J. Comb. Optim, 2011]. In this paper, we consider the substring-excluding constrained LCS (STR-EC-LCS) problem. A string Z is said to be an STR-EC-LCS of two given strings A and B excluding P if, Z is one of the longest common subsequences of A and B that does not contain P as a substring. Wang et al. proposed a dynamic programming solution which computes an STR-EC-LCS in O(mnr) time and space where \(m = |A|, n = |B|, r = |P|\) [Inf. Process. Lett., 2013]. In this paper, we show a new solution for the STR-EC-LCS problem. Our algorithm computes an STR-EC-LCS in \(O(n|\varSigma | + (L+1)(m-L+1)r)\) time where \(|\varSigma | \le \min \{m, n\}\) denotes the set of distinct characters occurring in both A and B, and L is the length of the STR-EC-LCS. This algorithm is faster than the O(mnr)-time algorithm for short/long STR-EC-LCS (namely, \(L \in O(1)\) or \(m-L \in O(1)\)), and is at least as efficient as the O(mnr)-time algorithm for all cases.

Notes

Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers JP18K18002 (YN), JP17H01697 (SI), JP16H02783 (HB), JP18H04098 (MT), and by JST PRESTO Grant Number JPMJPR1922 (SI).

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Kohei Yamada
    • 1
    Email author
  • Yuto Nakashima
    • 1
  • Shunsuke Inenaga
    • 1
    • 2
  • Hideo Bannai
    • 1
  • Masayuki Takeda
    • 1
  1. 1.Department of InformaticsKyushu UniversityFukuokaJapan
  2. 2.PRESTO, Japan Science and Technology AgencyKawaguchiJapan

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