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.
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Guillemot, S., Vialette, S. (2009). Pattern Matching for 321-Avoiding Permutations. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_107
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DOI: https://doi.org/10.1007/978-3-642-10631-6_107
Publisher Name: Springer, Berlin, Heidelberg
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