# Slides presented at 2016 Workshop über Algorithmen und Komplexität (Theorietag): "On the Benefit of Merging Suffix Array Intervals for Parallel Pattern Matching"

## 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 $p \leq m$. For approximate pattern matching with $k$ differences or mismatches, we show how to compute all occurrences of a given pattern in $O(\frac{m^k\sigma^k}{p} \max\{k, \lg\lg n\} + (1+m/p)\lg p \cdot \lg\lg n + occ)$ time, where $\sigma$ is the size of the alphabet and $p \leq \sigma^k m^k$. 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).