Chapter

Algorithms and Computation

Volume 5878 of the series Lecture Notes in Computer Science pp 1064-1073

Pattern Matching for 321-Avoiding Permutations

  • Sylvain GuillemotAffiliated withLIGM, CNRS UMR 8049, Université Paris-Est
  • , Stéphane VialetteAffiliated withLIGM, CNRS UMR 8049, Université Paris-Est

Abstract

Given two permutations π and σ, the NP-complete Permutation Pattern problem is to decide whether π contains σ as a pattern. In case both π and σ are 321-avoiding, we prove the Permutation Pattern problem to be solvable in O(k 2 n 6) time, where k = |σ| and n = |π|, and give a \(O(kn^{4\sqrt{k}+12})\) time algorithm if only σ is 321-avoiding. Finally, we show W[1]-hardness of a 2-colored version of this latter problem.