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 |
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Title of host publication | String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings |
Pages | 250-257 |
Number of pages | 8 |
DOIs | |
State | Published - 2010 |
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) |
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Volume | 6393 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 17th International Symposium on String Processing and Information Retrieval, SPIRE 2010 |
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Country/Territory | Mexico |
City | Los Cabos |
Period | 11/10/10 → 13/10/10 |
Bibliographical note
Funding Information:Supported by the Adams Fellowship of the Israel Academy of Sciences and Humanities. Partly supported by the National Science Foundation Award 0904246, Israel Science Foundation grants 35/05 and 347/09, the Israel-Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States-Israel Binational Science Foundation (BSF) and DFG. Partially supported by the Israel Science Foundation grant 1484/08.
Funding Information:
★Supported by the Adams Fellowship of the Israel Academy of Sciences and Humanities. ★★ Partly supported by the National Science Foundation Award 0904246, Israel Sci-ence Foundation grants 35/05 and 347/09, the Israel-Korea Scientific Research Cooperation, Yahoo, Grant No. 2008217 from the United States-Israel Binational Science Foundation (BSF) and DFG. ★★★ Partially supported by the Israel Science Foundation grant 1484/08.
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science