Generalized LCS

Amihood Amir; Tzvika Hartman; Oren Kapah; B. Riva Shalom; Dekel Tsur

doi:10.1016/j.tcs.2008.08.037

Generalized LCS

Amihood Amir
, Tzvika Hartman
, Oren Kapah
, B. Riva Shalom
, Dekel Tsur

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

The Longest Common Subsequence (LCS) is a well studied problem, having a wide range of implementations. Its motivation is in comparing strings. It has long been of interest to devise a similar measure for comparing higher dimensional objects, and more complex structures. In this paper we study the Longest Common Substructure of two matrices and show that this problem is N P-hard. We also study the Longest Common Subforest problem for multiple trees including a constrained version, as well. We show N P-hardness for k > 2 unordered trees in the constrained LCS. We also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees.

Original language	English
Pages (from-to)	438-449
Number of pages	12
Journal	Theoretical Computer Science
Volume	409
Issue number	3
DOIs	https://doi.org/10.1016/j.tcs.2008.08.037
State	Published - 28 Dec 2008

Bibliographical note

Funding Information:
The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.

Funding

The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.

Funders	Funder number
Israel Science Foundation	35/05

Keywords

Longest common subsequence
Matrices
Non crossing matching
Trees

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10.1016/j.tcs.2008.08.037

Cite this

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abstract = "The Longest Common Subsequence (LCS) is a well studied problem, having a wide range of implementations. Its motivation is in comparing strings. It has long been of interest to devise a similar measure for comparing higher dimensional objects, and more complex structures. In this paper we study the Longest Common Substructure of two matrices and show that this problem is N P-hard. We also study the Longest Common Subforest problem for multiple trees including a constrained version, as well. We show N P-hardness for k > 2 unordered trees in the constrained LCS. We also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees.",

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author = "Amihood Amir and Tzvika Hartman and Oren Kapah and Shalom, \{B. Riva\} and Dekel Tsur",

note = "Funding Information: The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.",

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doi = "10.1016/j.tcs.2008.08.037",

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AU - Hartman, Tzvika

AU - Kapah, Oren

AU - Shalom, B. Riva

AU - Tsur, Dekel

N1 - Funding Information: The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.

PY - 2008/12/28

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KW - Longest common subsequence

KW - Matrices

KW - Non crossing matching

KW - Trees

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Generalized LCS

Abstract

Bibliographical note

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Keywords

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