On the longest common parameterized subsequence

Abstract

a b s t r a c tThe well-known problem of the longest common subsequence (LCS), of two strings of lengths n and m respectively, is O(nm)-time solvable and is a classical distance measure for strings. Another well-studied string comparison measure is that of parameterized matching, where two equal-length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection. All works associated with parameterized pattern matching present polynomial time algorithms.There have been several attempts to accommodate parameterized matching along with other distance measures, as these turn out to be natural problems, e.g., Hamming distance, and a bounded version of edit-distance. Several algorithms have been proposed for these problems.In this paper we consider the longest common parameterized subsequence problem which combines the LCS measure with parameterized matching. We prove that the problem is NP-hard, and then show a couple of approximation algorithms for the problem.

An automated string-based approach to White Matter fiber-bundles clustering

“…In particular, within each such substring, the associated mapping function is required to be bijective. The work presented in [28] extends the approach in [27] by requiring the transformation function to have global validity. However, it still limits the set of allowed edit operations (in fact, substitutions are not allowed).…”

Longest common parameterized subsequences with fixed common substring

“…In order to prove that STR-IC-LCPS is NP-hard, we shall reduce LCPS (see [4] Let Σ ∪ Π be an alphabet. Let S 1 and S 2 are sequences over Σ ∪ Π.…”

“…We have consider our genetic algorithms OA [1] (see [24]), OA [2] (see [25]), OA [3] (see [26]), and OA [4] (see [27]) for SAT. We have used heterogeneous cluster.…”

“…Note that due to restrictions on computation time (20 hours) we used savepoints. Selected experimental results are given in Table 1. time average max best OA [1] 2.7 h 31.72 h 14 min OA [2] 2.32 h 26.4 h 18 min OA [3] 1.74 h 29 h 26 min OA [4] 1.96 h 14.4 h 21.2 min Table 1: Experimental results for STR-IC-LCPS.…”

The shortest common parameterized supersequence problem

“…Given sequences S 1 and S 2 over some fixed alphabet Σ ∪ Π, the longest common parameterized subsequence (LCPS) problem asks for a longest sequence T that is a parameterized subsequence of S 1 and S 2 . In [30] proved that LCPS is NP-hard. Note that by inserting the uncommon symbols (taking into account bijections) while preserving the symbol order, we can get a shortest common parameterized supersequence from longest common parameterized subsequence.…”