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 NPNP-Completeness. For the latter NPNP-hardness holds for two general unordered trees and for k trees in the constrained LCS.
| Original language | American English |
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| Title of host publication | International Symposium on String Processing and Information Retrieval |
| Editors | Nivio Ziviani, Ricardo Baeza-Yates |
| Publisher | Springer Berlin Heidelberg |
| State | Published - 2007 |