Generalized LCS

Authors:
Amihood Amir;Tzvika Hartman;Oren Kapah;B. Riva Shalom;Dekel Tsur
Affiliations:
Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel and Department of Computer Science, Johns Hopkins University, Baltimore, MD;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat-Gan, Israel;Department of Computer Science, Ben Gurion University, Be'er Sheva, Israel
Venue:
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Year:
2007

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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 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-Completeness. For the latter NP-hardness holds for two general unordered trees and for k trees in the constrained LCS.