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Space-Efficient STR-IC-LCS Computation

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SOFSEM 2023: Theory and Practice of Computer Science (SOFSEM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13878))

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Abstract

One of the most fundamental methods for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of the longest common subsequence. In this paper, we address the STR-IC-LCS problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is one of the longest common subsequences of A and B that contains P as a substring. We present a space efficient solution for the STR-IC-LCS problem. Our algorithm computes the length of an STR-IC-LCS in \(O(n^2)\) time and \(O((\ell +1)(n-\ell +1))\) space where \(\ell \) is the length of a longest common subsequence of A and B of length n. When \(\ell = O(1)\) or \(n-\ell = O(1)\), then our algorithm uses only linear O(n) space.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers JP21K17705 (YN), JP22H03551 (SI), JP20H04141 (HB), and by JST PRESTO Grant Number JPMJPR1922 (SI).

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Authors and Affiliations

  1. Department of Information Science and Technology, Kyushu University, Fukuoka, Japan

    Yuuki Yonemoto

  2. Department of Informatics, Kyushu University, Fukuoka, Japan

    Yuto Nakashima & Shunsuke Inenaga

  3. PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan

    Shunsuke Inenaga

  4. M &D Data Science Center, Tokyo Medical and Dental University, Tokyo, Japan

    Hideo Bannai

Authors
  1. Yuuki Yonemoto
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  2. Yuto Nakashima
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  3. Shunsuke Inenaga
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  4. Hideo Bannai
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Corresponding author

Correspondence to Yuto Nakashima .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Leszek Gąsieniec

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Yonemoto, Y., Nakashima, Y., Inenaga, S., Bannai, H. (2023). Space-Efficient STR-IC-LCS Computation. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_25

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  • DOI: https://doi.org/10.1007/978-3-031-23101-8_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-23100-1

  • Online ISBN: 978-3-031-23101-8

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