Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences

02/17/2020

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by   Mitsuru Funakoshi, et al.

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The equidistant subsequence pattern matching problem is considered. Given a pattern string P and a text string T, we say that P is an equidistant subsequence of T if P is a subsequence of the text such that consecutive symbols of P in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield o(n^2) time algorithms for finding k-(sub-)cadences and equidistant subsequences. Furthermore, O(nlog^2 n) and O(nlog n) time algorithms, respectively for equidistant and Abelian equidistant matching for the case |P| = 3, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints.