On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching

TL;DR

This paper introduces parallel algorithms for exact and approximate pattern matching using suffix arrays, focusing on efficient interval merging with a novel data structure, enabling faster processing on parallel architectures.

Contribution

It presents a new data structure for quickly merging suffix array intervals and parallel algorithms for pattern matching, improving efficiency over previous methods.

Findings

Parallel suffix array interval computation in sub-logarithmic time.

Efficient merging of suffix array intervals in constant or near-constant parallel time.

Algorithms handle approximate matching with up to k differences efficiently.

Abstract

We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given pattern of length $m$ in $O(\frac{m}{p}+ \lg p + \lg\lg p\cdot\lg\lg n)$ time for $p \le m$. For approximate pattern matching with $k$ differences or mismatches, we show how to compute all occurrences of a given pattern in $O(\frac{m^k\sigma^k}{p}\max\left(k,\lg\lg n\right)\!+\!(1+\frac{m}{p}) \lg p\cdot \lg\lg n + \text{occ})$ time, where $\sigma$ is the size of the alphabet and $p \le \sigma^k m^k$. The workhorse of our algorithms is a data structure for merging suffix array intervals quickly: Given the suffix array intervals for two patterns $P$ and $P'$, we present a data structure for computing the interval of $PP'$ in $O(\lg\lg n)$ sequential time, or in $O(1+\lg_p\lg n)$ parallel time. All our data structures are of size $O(n)$ bits (in addition to the suffix array).