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.
|Title of host publication
|String Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings
|Number of pages
|Published - 2007
|14th International Symposium on String Processing and Information Retrieval, SPIRE 2007 - Santiago, Chile
Duration: 29 Oct 2007 → 31 Oct 2007
|Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
|14th International Symposium on String Processing and Information Retrieval, SPIRE 2007
|29/10/07 → 31/10/07
Bibliographical noteFunding Information:
The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.