Faster Algorithms for Computing Longest Common Increasing Subsequences

Martin Kutz, Gerth Stølting Brodal, Kanela Kaligosi, and Irit Katriel

In Journal of Discrete Algorithms, Special Issue of CPM 2006, volume 9(4), pages 314-325, 2011.


We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where mn, we present an algorithm with an output-dependent expected running time of O((m+nl) loglog σ + Sort) and O(m) space, where l is the length of an LCIS, σ is the size of the alphabet, and Sort is the time to sort each input sequence. For k≥ 3 length-n sequences we present an algorithm which improves the previous best bound by more than a factor k for many inputs. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an O(min{m+nlog n,mloglog m})-time algorithm for the 3-letter alphabet case. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small alphabets.

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Copyright © 2010 by Elsevier Inc.. All rights reserved.

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BIBTEX entry

  author = "Martin Kutz and Gerth St{\o}lting Brodal and Kanela Kaligosi and Irit Katriel",
  doi = "10.1016/j.jda.2011.03.013",
  issn = "1570-8667",
  journal = "Journal of Discrete Algorithms, Special Issue of CPM 2006",
  number = "4",
  pages = "314-325",
  publisher = "Elsevier Science",
  title = "Faster Algorithms for Computing Longest Common Increasing Subsequences",
  volume = "9",
  year = "2011"

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