Longest common parameterized subsequences with fixed common substring

Abstract

In this paper we consider the problem of the longest common parameterized subsequence with fixed common substring (STR-IC-LCPS). In particular, we show that STR-IC-LCPS is NP-complete. We describe an approach to solve STR-IC-LCPS. This approach is based on an explicit reduction from the problem to the satisfiability problem.

On the shortest common parameterized supersequence problem

“…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 (see e.g. [1,2]). For instance, it is considered the periodicity of parameterized strings.…”

Longest common parameterized subsequences with parameterized common substring

“…A well-studied string comparison measure is that of parameterized matching (basic definitions and results can be found in [1]). In particular, the problem of the longest common parameterized subsequence with fixed common substring (STR-IC-LCPS) was proposed in [2]. In this paper we consider the problem of the longest common parameterized subsequence with parameterized common substring (PSTR-IC-LCPS).…”

“…Note that if P is a string over Σ, then an instance of PSTR-IC-LCPS is an instance of STR-IC-LCPS. Therefore, in view of NP-completeness of STR-IC-LCPS (see [2]), it is easy to see that PSTR-IC-LCPS is NP-complete. Encoding different hard problems as instances of different variants of the satisfiability problem and solving them with very efficient satisfiability algorithms has caused considerable interest (see e.g.…”

“…We have designed generators of natural instances for PSTR-IC-LCPS. We consider our genetic algorithms OA [1] (see [23]), OA [2] (see [24]), OA [3] (see [25]), and OA [4] (see [26]) for SAT. We 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] 2.63 h 33.54 h 23.81 min OA [2] 3.61 h 39.12 h 27.14 min OA [3] 4.26 h 43.28 h 24.29 min OA [4] 3.78 h 28.72 h 17.43 min Table 1: Experimental results for PSTR-IC-LCPS.…”