Linear pattern matching on sparse suffix trees

TL;DR

This paper introduces a space-efficient index for packed strings based on sparse suffix trees, enabling faster pattern matching by exploiting character packing within computer words.

Contribution

It proposes a novel index structure for packed strings using sparse suffix trees with suffix links, achieving optimal space and improved pattern matching performance.

Findings

Index uses O(n/ log_sigma n) space, matching packed string size.

Pattern matching runs in O(m + r^2 + r * occ) time, with r characters per word.

Efficiently exploits character packing for faster string processing.

Abstract

Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse suffix tree} \cite{KU-96} with appropriately defined suffix links. Assuming, under the standard unit-cost RAM model, that a word can store up to $\log_{\sigma}n$ characters ($\sigma$ the alphabet size), our index takes $O(n/\log_{\sigma}n)$ space, i.e. the same space as the packed string itself. The resulting pattern matching algorithm runs in time $O(m+r^2+r\cdot occ)$, where $m$ is the length of the pattern, $r$ is the actual number of characters stored in a word and $occ$ is the number of pattern occurrences.