Streaming Pattern Matching with d Wildcards release_uj56nfjx7zc4fbwyq43c5cdn6q

by Shay Golan, Tsvi Kopelowitz, Ely Porat

Released as a article .

2017  

Abstract

In the pattern matching with d wildcards problem one is given a text T of length n and a pattern P of length m that contains d wildcard characters, each denoted by a special symbol '?'. A wildcard character matches any other character. The goal is to establish for each m-length substring of T whether it matches P. In the streaming model variant of the pattern matching with d wildcards problem the text T arrives one character at a time and the goal is to report, before the next character arrives, if the last m characters match P while using only o(m) words of space. In this paper we introduce two new algorithms for the d wildcard pattern matching problem in the streaming model. The first is a randomized Monte Carlo algorithm that is parameterized by a constant 0≤δ≤ 1. This algorithm uses Õ(d^1-δ) amortized time per character and Õ(d^1+δ) words of space. The second algorithm, which is used as a black box in the first algorithm, is a randomized Monte Carlo algorithm which uses O(d+ m) worst-case time per character and O(d m) words of space.
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Type  article
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Date   2017-04-05
Version   v1
Language   en ?
arXiv  1704.01646v1
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