On shortest common superstring and swap permutations

Zvi Gotthilf, Moshe Lewenstein, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

The Shortest Common Superstring (SCS) is a well studied problem, having a wide range of applications. In this paper we consider two problems closely related to it. First we define the Swapped Restricted Superstring(SRS) problem, where we are given a set S of n strings, s1, s2, ..., sn , and a text T=t1 t2 ...tm , and our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the number of strings in S that are substrings of tπ(1) tπ(2)...tπ(m). We then show that the SRS problem is NP-Complete. Afterwards, we consider a similar variant denoted SRSR, where our goal is to find a swap permutation π: {1, ..., m} →{1, ..., m} to maximize the total number of times that the strings of S appear in t π(1) tπ(2)...tπ(m) (we can count the same string si as a substring of tπ(1) t π(2)...tπ(m) more than once). For this problem, we present a polynomial time exact algorithm.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings
Pages270-278
Number of pages9
DOIs
StatePublished - 2010
Event17th International Symposium on String Processing and Information Retrieval, SPIRE 2010 - Los Cabos, Mexico
Duration: 11 Oct 201013 Oct 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6393 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Symposium on String Processing and Information Retrieval, SPIRE 2010
Country/TerritoryMexico
CityLos Cabos
Period11/10/1013/10/10

Bibliographical note

Funding Information:
★ This work was partially supported by the Israel Science Foundation grant 1484/08.

Funding Information:
Acknowledgements. We thank the anonymous reviewers for their useful comments. The third author is funded by an EPSRC PhD studentship.

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