Generalized LCS

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

doi:10.1007/978-3-540-75530-2_5

Generalized LCS

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

Department of Computer Science

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

7 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 give, what is to our knowledge, the first inherently multi-dimensional definition of LCS. We discuss the Longest Common Substructure of two matrices and the Longest Common Subtree problem for multiple trees including a constrained version. Both problems cannot be solved by a natural extension of the original LCS solution. We investigate the tractability of the above problems. For the first we prove NP-Conipleteness. For the latter NP-hardness holds for two general unordered trees and for k trees in the constrained LCS.

Original language	English
Title of host publication	String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings
Publisher	Springer Verlag
Pages	50-61
Number of pages	12
ISBN (Print)	9783540755296
DOIs	https://doi.org/10.1007/978-3-540-75530-2_5
State	Published - 2007
Event	14th International Symposium on String Processing and Information Retrieval, SPIRE 2007 - Santiago, Chile Duration: 29 Oct 2007 → 31 Oct 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4726 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th International Symposium on String Processing and Information Retrieval, SPIRE 2007
Country/Territory	Chile
City	Santiago
Period	29/10/07 → 31/10/07

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
Iowa Science Foundation	35/05

Access to Document

10.1007/978-3-540-75530-2_5

Cite this

Amir, A., Hartman, T., Kapah, O., Shalom, B. R., & Tsur, D. (2007). Generalized LCS. In String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings (pp. 50-61). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4726 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-75530-2_5

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title = "Generalized LCS",

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 give, what is to our knowledge, the first inherently multi-dimensional definition of LCS. We discuss the Longest Common Substructure of two matrices and the Longest Common Subtree problem for multiple trees including a constrained version. Both problems cannot be solved by a natural extension of the original LCS solution. We investigate the tractability of the above problems. For the first we prove NP-Conipleteness. For the latter NP-hardness holds for two general unordered trees and for k trees in the constrained LCS.",

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.; 14th International Symposium on String Processing and Information Retrieval, SPIRE 2007 ; Conference date: 29-10-2007 Through 31-10-2007",

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Amir, A, Hartman, T, Kapah, O, Shalom, BR & Tsur, D 2007, Generalized LCS. in String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4726 LNCS, Springer Verlag, pp. 50-61, 14th International Symposium on String Processing and Information Retrieval, SPIRE 2007, Santiago, Chile, 29/10/07. https://doi.org/10.1007/978-3-540-75530-2_5

Generalized LCS. / Amir, Amihood; Hartman, Tzvika; Kapah, Oren et al.
String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings. Springer Verlag, 2007. p. 50-61 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4726 LNCS).

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

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AU - Amir, Amihood

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 - 2007

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AB - 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 give, what is to our knowledge, the first inherently multi-dimensional definition of LCS. We discuss the Longest Common Substructure of two matrices and the Longest Common Subtree problem for multiple trees including a constrained version. Both problems cannot be solved by a natural extension of the original LCS solution. We investigate the tractability of the above problems. For the first we prove NP-Conipleteness. For the latter NP-hardness holds for two general unordered trees and for k trees in the constrained LCS.

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ER -

Generalized LCS

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