On-line weighted pattern matching

https://doi.org/10.1016/j.ic.2019.01.001Get rights and content
Under an Elsevier user license
open archive

Abstract

A weighted sequence is a sequence of probability distributions over an alphabet of size σ. Weighted sequences arise naturally in many applications. We study the problem of weighted pattern matching in which we are given a string pattern P of length m, a weight threshold 1z, and a weighted text X arriving on-line. We say that P occurs in X at position i if the product of probabilities of the letters of P at positions im+1,,i in X is at least 1z. We first discuss how to apply a known general scheme that transforms off-line pattern matching algorithms to on-line algorithms to obtain an on-line algorithm that requires O((σ+logz)logm) or O(σlog2m) time per arriving position; with the space requirement however being O(mmin(σ,z)). Our main result is a new algorithm that processes each arriving position of X in O(z+σ) time using O(m+z) extra space.

Keywords

Weighted sequence
Position weight matrix (PWM)
Uncertain sequence
On-line pattern matching
String matching automaton

Cited by (0)