Streaming Pattern Matching with d Wildcards
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by
Shay Golan, Tsvi Kopelowitz, Ely Porat
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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