Restricted common superstring and restricted common supersequence

Raphaël Clifford, Zvi Gotthilf, Moshe Lewenstein, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

The shortest common superstring and the shortest common supersequence are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly RCSstr) problem and the Restricted Common Supersequence (shortly RCSseq). In the RCSstr (RCSseq) problem we are given a set S of n strings, s 1, s 2, ..., s n , and a multiset t = {t 1, t 2, ..., t m }, and the goal is to find a permutation π: {1, ..., m} → {1, ..., m} to maximize the number of strings in S that are substrings (subsequences) of π(t) = t π(1) t π(2) ⋯ t π(m) (we call this ordering of the multiset, π(t), a permutation of t). We first show that in its most general setting the RCSstr problem is NP-complete and hard to approximate within a factor of n 1 - ε , for any ε > 0, unless P = NP. Afterwards, we present two separate reductions to show that the RCSstr problem remains NP-Hard even in the case where the elements of t are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the RCSstr problem. In the second part of this paper, we turn to the RCSseq problem, where we present some hardness results, tight lower bounds and approximation algorithms.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 22nd Annual Symposium, CPM 2011, Proceedings
Pages467-478
Number of pages12
DOIs
Publication statusPublished - Jul 13 2011
Event22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011 - Palermo, Italy
Duration: Jun 27 2011Jun 29 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6661 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd Annual Symposium on Combinatorial Pattern Matching, CPM 2011
CountryItaly
CityPalermo
Period6/27/116/29/11

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Clifford, R., Gotthilf, Z., Lewenstein, M., & Popa, A. (2011). Restricted common superstring and restricted common supersequence. In Combinatorial Pattern Matching - 22nd Annual Symposium, CPM 2011, Proceedings (pp. 467-478). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6661 LNCS). https://doi.org/10.1007/978-3-642-21458-5_39