String Matching with Wildcards in the Massively Parallel Computation Model

TL;DR

This paper develops efficient parallel algorithms within the MPC framework for string matching problems involving wildcards, addressing '?' (don't cares), '+' (repetitions), and '*' (any substring) with constant or logarithmic round complexity.

Contribution

It introduces novel MPC algorithms for string matching with wildcards, utilizing FFT and reductions, achieving constant or logarithmic rounds for different wildcard types.

Findings

Constant round MPC algorithm for '?' wildcard matching using FFT.

Constant round MPC algorithm for '+' wildcard matching via reduction from subset matching.

Logarithmic round algorithms for '*' wildcard matching in specific cases.

Abstract

We study distributed algorithms for string matching problem in presence of wildcard characters. Given a string T (a text), we look for all occurrences of another string P (a pattern) as a substring of string T . Each wildcard character in the pattern matches a specific class of strings based on its type. String matching is one of the most fundamental problems in computer science, especially in the fields of bioinformatics and machine learning. Persistent effort has led to a variety of algorithms for the problem since 1960s. With rise of big data and the inevitable demand to solve problems on huge data sets, there have been many attempts to adapt classic algorithms into the MPC framework to obtain further efficiency. MPC is a recent framework for parallel computation of big data, which is designed to capture the MapReduce-like algorithms. In this paper, we study the string matching problem using a set of tools translated to MPC model. We consider three types of wildcards in string matching: - '?' wildcard: In this setting, the pattern is allowed to contain special '?' characters or don't cares that match any character of the text. String matching with don't cares could be solved by fast convolutions, and we give a constant round MPC algorithm for which by utilizing FFT in a constant number of MPC rounds. - '+' wildcard: '+' wildcard is a special character that allows for arbitrary repetitions of a character. When the pattern contains '+' wildcard characters, our algorithm runs in a constant number of MPC rounds by a reduction from subset matching problem. - '*' wildcard: '*' is a special character that matches with any substring of the text. When '*' is allowed in the pattern, we solve two special cases of the problem in logarithmic rounds.