On shortest common superstring and swap permutations

  • Authors:

  • Zvi Gotthilf;Moshe Lewenstein;Alexandru Popa

  • Affiliations:

  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel;Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel;Department of Computer Science, University of Bristol, UK

  • Venue:
  • SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
  • Year:
  • 2010

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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 = t1t2 . . . 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 tπ(1)tπ(2) . . . tπ(m) (we can count the same string si as a substring of tπ(1)tπ(2) . . . tπ(m) more than once). For this problem, we present a polynomial time exact algorithm.