## 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, s_{1}, s_{2}, ..., s_{n} , and a text T=t_{1} t_{2} ...t_{m} , 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 t_{π(1)} t_{π(2)}...t_{π(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)} t_{π(2)}...t_{π(m)} (we can count the same string s_{i} as a substring of t_{π(1)} t _{π(2)}...t_{π(m)} more than once). For this problem, we present a polynomial time exact algorithm.

Original language | English |
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Title of host publication | String Processing and Information Retrieval - 17th International Symposium, SPIRE 2010, Proceedings |

Pages | 270-278 |

Number of pages | 9 |

DOIs | |

State | Published - 2010 |

Event | 17th International Symposium on String Processing and Information Retrieval, SPIRE 2010 - Los Cabos, Mexico Duration: 11 Oct 2010 → 13 Oct 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6393 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 17th International Symposium on String Processing and Information Retrieval, SPIRE 2010 |
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Country/Territory | Mexico |

City | Los Cabos |

Period | 11/10/10 → 13/10/10 |

### 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.