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Computer Science > Data Structures and Algorithms

arXiv:1609.03668 (cs)
[Submitted on 13 Sep 2016 (v1), last revised 6 Feb 2017 (this version, v3)]

Title:Longest Common Subsequence in at Least $k$ Length Order-Isomorphic Substrings

Authors:Yohei Ueki, Diptarama, Masatoshi Kurihara, Yoshiaki Matsuoka, Kazuyuki Narisawa, Ryo Yoshinaka, Hideo Bannai, Shunsuke Inenaga, Ayumi Shinohara
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Abstract:We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a better worst-case running time than existing algorithms, where $m$ and $n$ are lengths of the input strings. Furthermore, we mainly consider the LCS in at least $k$ length order-isomorphic substrings problem. We show that the problem can also be solved in $O(mn)$ worst-case time by an easy-to-implement algorithm.
Comments: 14 pages, 7 figures, contains erratum to Springer's version (SOFSEM 2017)
Subjects: Data Structures and Algorithms (cs.DS)
Cite as: arXiv:1609.03668 [cs.DS]
  (or arXiv:1609.03668v3 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1609.03668

Submission history

From: Yohei Ueki [view email]
[v1] Tue, 13 Sep 2016 03:54:52 UTC (554 KB)
[v2] Sat, 29 Oct 2016 15:41:58 UTC (458 KB)
[v3] Mon, 6 Feb 2017 05:43:08 UTC (458 KB)
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