A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

  • Marie-Louise Bruner
  • Martin Lackner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7357)

Abstract

The NP-complete Permutation Pattern Matching problem asks whether a permutation P can be matched into a permutation T. A matching is an order-preserving embedding of P into T. We present a fixed-parameter algorithm solving this problem with an exponential worst-case runtime of \(\mathcal{O}^*(1.79^{\sf{run}(T)})\), where run(T) denotes the number of alternating runs of T. This is the first algorithm that improves upon the \(\mathcal{O}^*(2^n)\) runtime required by brute-force search without imposing restrictions on P and T. Furthermore we prove that – under standard complexity theoretic assumptions – such a fixed-parameter tractability result is not possible for run(P).

Keywords

Dynamic Programming Algorithm Matching Function Representative Element Permutation Graph Pattern Avoidance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marie-Louise Bruner
    • 1
  • Martin Lackner
    • 2
  1. 1.Institute of Discrete Mathematics and GeometryVienna University of TechnologyAustria
  2. 2.Institute of Information SystemsVienna University of TechnologyAustria

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