Generalized LCS

Abstract

a b s t r a c tThe 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 N P -hard. We also study the Longest Common Subforest problem for multiple trees including a constrained version, as well. We show N P -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.

Theoretical Framework for Eliminating Redundancy in Workflows

“…Our set of problems are very different from the traditional LCS problems for higher dimensional structures [15,1]. All of them are duals of the edit distance problem and our problems aren't.…”

“…We continue the same process again. However, we found that this LCS(T (i), C(j)) = ( T (i) = C(j) LCS(lef t(T (i)), C(j + 1)) + LCS(right(T (i)), C(j + 1)) + 1 T (i) = C(j) max(LCS(T (i), C(j + 1)), (LCS(lef t(T (i)), C(j)) + LCS(right(T (i)), C(j)))) (1) approach was also not sufficient. At some point, we unmerge all the vertices and start from scratch.…”

“…Sadly other than the basic LCS problem and variants of it like TreeLCS [15], other problems have either not deserved enough attention or have been proven to be NP-Complete. For example, a recent paper [1] generalizes LCS to matrices and forests, and proves both the problems to be NP Complete.…”

“…There is one similarity in the definition of LCS for higher dimensional structures in all the previous works [1,15]. Their variant of LCS is the dual of the minimum edit distance problem, which can be stated as follows.…”

Unranked Anti-Unification with Hedge and Context Variables

“…Next, it inserts context and/or hedge variables into the skeleton, which are supposed to uniformly generalize (vertical and horizontal) differences between input hedges, to obtain an lgg (with respect to the given skeleton). The skeleton computation function is the parameter of the algorithm: One can compute an lgg which contains, for instance, a constrained longest common subforest [1], or an agreement subhedge/subtree [5] of the input hedges.…”