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 \(\cal{NP}\)-Completeness. For the latter \(\cal{NP}\)-hardness holds for two general unordered trees and for k trees in the constrained LCS.
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Amir, A., Hartman, T., Kapah, O., Shalom, B.R., Tsur, D. (2007). Generalized LCS. In: Ziviani, N., Baeza-Yates, R. (eds) String Processing and Information Retrieval. SPIRE 2007. Lecture Notes in Computer Science, vol 4726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75530-2_5
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DOI: https://doi.org/10.1007/978-3-540-75530-2_5
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