Faster Algorithms for Computing Longest Common Increasing Subsequences

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

In Proc. 17th Annual Symposium on Combinatorial Pattern Matching, volume 4009 of Lecture Notes in Computer Science, pages 330-341. Springer Verlag, Berlin, 2006.


We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths m and n, 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(m+nlog n)-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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© Springer-Verlag Berlin Heidelberg 2006. All rights reserved.

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BIBTEX entry

  author = "Gerth St{\o}lting Brodal and Kanela Kaligosi and Irit Katriel and Martin Kutz",
  booktitle = "Proc. 17th Annual Symposium on Combinatorial Pattern Matching",
  doi = "10.1007/11780441_30",
  isbn = "978-3-540-35455-0",
  pages = "330-341",
  publisher = "Springer {V}erlag, Berlin",
  series = "Lecture Notes in Computer Science",
  title = "Faster Algorithms for Computing Longest Common Increasing Subsequences",
  volume = "4009",
  year = "2006"