Restricted LCS

Zvi Gotthilf; Danny Hermelin; Gad M. Landau; Moshe Lewenstein

doi:10.1007/978-3-642-16321-0_26

Restricted LCS

Zvi Gotthilf, Danny Hermelin, Gad M. Landau, Moshe Lewenstein

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

36 Scopus citations

Abstract

The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more constraint strings as subsequences, the problem becomes the Constrained LCS (CLCS) problem. In this paper we consider the Restricted LCS (RLCS) problem, where our goal is finding a longest common subsequence between two or more strings that does not contain a given set of restriction strings as subsequences. First we show that in case of two input strings and an arbitrary number of restriction strings the RLCS problem is NP-hard. Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings. In the last part of this paper we present two approximation algorithms for the hard variants of the problem.

Original language	English
Title of host publication	String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings
Pages	250-257
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-642-16321-0_26
State	Published - 24 Nov 2010
Externally published	Yes
Event	17th International Symposium on String Processing and Information Retrieval, SPIRE 2010 - Los Cabos, Mexico Duration: 11 Oct 2010 → 13 Oct 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6393 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	17th International Symposium on String Processing and Information Retrieval, SPIRE 2010
Country/Territory	Mexico
City	Los Cabos
Period	11/10/10 → 13/10/10

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-16321-0_26

Cite this

Gotthilf, Z., Hermelin, D., Landau, G. M., & Lewenstein, M. (2010). Restricted LCS. In String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings (pp. 250-257). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6393 LNCS). https://doi.org/10.1007/978-3-642-16321-0_26

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Gotthilf, Z, Hermelin, D, Landau, GM & Lewenstein, M 2010, Restricted LCS. in String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6393 LNCS, pp. 250-257, 17th International Symposium on String Processing and Information Retrieval, SPIRE 2010, Los Cabos, Mexico, 11/10/10. https://doi.org/10.1007/978-3-642-16321-0_26

Restricted LCS. / Gotthilf, Zvi; Hermelin, Danny; Landau, Gad M. et al.
String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings. 2010. p. 250-257 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6393 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Hermelin, Danny

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N2 - The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more constraint strings as subsequences, the problem becomes the Constrained LCS (CLCS) problem. In this paper we consider the Restricted LCS (RLCS) problem, where our goal is finding a longest common subsequence between two or more strings that does not contain a given set of restriction strings as subsequences. First we show that in case of two input strings and an arbitrary number of restriction strings the RLCS problem is NP-hard. Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings. In the last part of this paper we present two approximation algorithms for the hard variants of the problem.

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Restricted LCS

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