Algorithms for three versions of the shortest common superstring problem

  • Authors:

  • Maxime Crochemore;Marek Cygan;Costas Iliopoulos;Marcin Kubica;Jakub Radoszewski;Wojciech Rytter;Tomasz Waleń

  • Affiliations:

  • King's College London, London, UK and Université Paris-Est, France;Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland;King's College London, London, UK and Digital Ecosystems & Business Intelligence Institute, Curtin University of Technology, Perth, WA, Australia;Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland;Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland;Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland and Dept. of Math. and Informatics, Copernicus University, Toruń, Poland;Dept. of Mathematics, Computer Science and Mechanics, University of Warsaw, Warsaw, Poland

  • Venue:
  • CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
  • Year:
  • 2010

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Abstract

The input to the Shortest Common Superstring (SCS) problem is a set S of k words of total length n. In the classical version the output is an explicit word SCS(S) in which each s ∈ S occurs at least once. In our paper we consider two versions with multiple occurrences, in which the input includes additional numbers (multiplicities), given in binary. Our output is the word SCS(S) given implicitly in a compact form, since its real size could be exponential. We also consider a case when all input words are of length two, where our main algorithmic tool is a compact representation of Eulerian cycles in multigraphs. Due to exponential multiplicities of edges such cycles can be exponential and the compact representation is needed. Other tools used in our paper are a polynomial case of integer linear programming and a min-plus product of matrices.