Faster Exponential Algorithm for Permutation Pattern Matching

Abstract

The Permutation Pattern Matching problem asks, given two permutations σ on n elements and π, whether σ admits a subsequence with the same relative order as π (or, in the counting version, how many such subsequences are there). This natural problem was shown by Bose, Buss and Lubiw [IPL 1998] to be NP-complete, and hence we should seek exact exponential time solutions. The asymptotically fastest such solution up to date, by Berendsohn, Kozma and Marx [IPEC 2019], works in O(1.6181 n ) time. We design a simple and faster O(1.415 n ) time algorithm for both the detection and the counting version. We also prove that this is optimal among a certain natural class of algorithms.