Generalized LCS
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 study the Longest Common Substructure of two matrices and show that this problem is NP-hard. We also study the Longest Common Subforest problem for multiple trees including a constrained version, as well. We show NP-hardness for k > 2 unordered trees in the constrained LCS. We also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees. (C) 2008 Elsevier B.V. All rights reserved.
longest common subsequence matrices trees non crossing matching