Restricted lcs

Z Gotthilf; D Hermelin; G. M Landau; M Lewenstein

Restricted lcs

Z Gotthilf, D Hermelin, G. M Landau, M Lewenstein

Department of Computer Science

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

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	American English
Title of host publication	International Symposium on String Processing and Information Retrieval
Editors	Edgar Chavez, Stefano Lonardi
Publisher	Springer Berlin Heidelberg
State	Published - 2010

Bibliographical note

Place of conference:Mexico

Cite this

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title = "Restricted lcs",

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.",

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year = "2010",

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editor = "Edgar Chavez and Stefano Lonardi",

booktitle = "International Symposium on String Processing and Information Retrieval",

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T1 - Restricted lcs

AU - Gotthilf, Z

AU - Hermelin, D

AU - Landau, G. M

AU - Lewenstein, M

N1 - Place of conference:Mexico

PY - 2010

Y1 - 2010

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.

AB - 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.

UR - https://scholar.google.co.il/scholar?q=Restricted+LCS&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - International Symposium on String Processing and Information Retrieval

A2 - Chavez, Edgar

A2 - Lonardi, Stefano

PB - Springer Berlin Heidelberg

ER -

Restricted lcs

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