Pattern Matching For K-Track Permutations
COMBINATORIAL ALGORITHMS, IWOCA 2018(2018)
摘要
Given permutations tau and pi, the permutation pattern (PP) problem is to decide whether pi occurs in tau as an order-isomorphic subsequence. Although an FPT algorithm is known for PP parameterized by the size of the pattern vertical bar pi vertical bar [Guillemot and Marx 2014], the high complexity of this algorithm makes it impractical for most instances. In this paper we approach the PP problem from k-track permutations, i.e. those permutations that are the union of k increasing patterns or, equivalently, those permutation that avoid the decreasing pattern (k+ 1) k...1. Recently, k-track permutations have been shown to be central combinatorial objects in the study of the PP problem. Indeed, the PP problem is NP-complete when pi is 321-avoiding and tau is 4321-avoiding but is solvable in polynomial-time if both pi and tau avoid 321. We propose and implement an exact algorithm, FPT for parameters k and vertical bar pi vertical bar, which allows to solve efficiently some large instances.
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关键词
pattern matching,k-track
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