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Faster STR-IC-LCS Computation via RLE

Authors: Keita Kuboi, Yuta Fujishige, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

The constrained LCS problem asks one to find a longest common subsequence of two input strings A and B with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given constraint string C as a substring. Given two strings A and B of respective lengths M and N, and a constraint string C of length at most min{M, N}, the best known algorithm for the STR-IC-LCS problem, proposed by Deorowicz (Inf. Process. Lett., 11:423-426, 2012), runs in O(MN) time. In this work, we present an O(mN + nM)-time solution to the STR-IC-LCS problem, where m and n denote the sizes of the run-length encodings of A and B, respectively. Since m <= M and n <= N always hold, our algorithm is always as fast as Deorowicz's algorithm, and is faster when input strings are compressible via RLE.

Cite as

Keita Kuboi, Yuta Fujishige, Shunsuke Inenaga, Hideo Bannai, and Masayuki Takeda. Faster STR-IC-LCS Computation via RLE. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 20:1-20:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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  author =	{Kuboi, Keita and Fujishige, Yuta and Inenaga, Shunsuke and Bannai, Hideo and Takeda, Masayuki},
  title =	{{Faster STR-IC-LCS Computation via RLE}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{20:1--20:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.20},
  URN =		{urn:nbn:de:0030-drops-73335},
  doi =		{10.4230/LIPIcs.CPM.2017.20},
  annote =	{Keywords: longest common subsequence, STR-IC-LCS, run-length encoding}
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