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Duel and sweep algorithm for order-preserving pattern matching

Abstract

Given a text TT and a pattern PP over alphabet Σ\Sigma, the classic exact matching problem searches for all occurrences of pattern PP in text TT. Unlike exact matching problem, order-preserving pattern matching (OPPM) considers the relative order of elements, rather than their real values. In this paper, we propose an efficient algorithm for OPPM problem using the "duel-and-sweep" paradigm. Our algorithm runs in O(n+mlogm)O(n + m\log m) time in general and O(n+m)O(n + m) time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster that KMP-based algorithm. Last, we introduce the two-dimensional order preserved pattern matching and give a duel and sweep algorithm that runs in O(n2)O(n^2) time for duel stage and O(n2m)O(n^2 m) time for sweeping time with O(m3)O(m^3) preprocessing time.Comment: 13 pages, 5 figure

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