Pattern Matching for k-Track Permutations

  • Laurent Bulteau
  • Romeo Rizzi
  • Stéphane VialetteEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)


Given permutations \(\tau \) and \(\pi \), the permutation pattern (PP) problem is to decide whether \(\pi \) occurs in \(\tau \) as an order-isomorphic subsequence. Although an FPT algorithm is known for PP parameterized by the size of the pattern \(|\pi |\) [Guillemot and Marx 2014], the high complexity of this algorithm makes it impractical for most instances. In this paper we approach the PP problem from k-track permutations, i.e. those permutations that are the union of k increasing patterns or, equivalently, those permutation that avoid the decreasing pattern \((k+1) k \ldots 1\). Recently, k-track permutations have been shown to be central combinatorial objects in the study of the PP problem. Indeed, the PP problem is NP-complete when \(\pi \) is 321-avoiding and \(\tau \) is 4321-avoiding but is solvable in polynomial-time if both \(\pi \) and \(\tau \) avoid 321. We propose and implement an exact algorithm, FPT for parameters k and \(|\pi |\), which allows to solve efficiently some large instances.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Laurent Bulteau
    • 1
  • Romeo Rizzi
    • 2
  • Stéphane Vialette
    • 1
    Email author
  1. 1.Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEMMarne-la-ValléeFrance
  2. 2.Department of Computer ScienceUniversity of VeronaVeronaItaly

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