A fast algorithm for permutation pattern matching based on alternating runs

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 , where run(T) denotes the number of alternating runs of T. This is the first algorithm that improves upon the 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). © 2012 Springer-Verlag.