Deterministic Indexing for Packed Strings

TL;DR

This paper introduces a deterministic, space-efficient string index for packed strings that enables faster pattern matching queries by leveraging multiple characters stored in single machine words.

Contribution

It presents the first deterministic index for packed strings with optimal preprocessing and improved query times based on character packing density.

Findings

Preprocessing time and space are both O(n).

Query time improves with increased character packing in words.

The index matches or surpasses previous bounds, especially with dense packing.

Abstract

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string indexing problem without any randomization (at preprocessing time or query time). In the \emph{packed} variant the strings are stored with several character in a single word, giving us the opportunity to read multiple characters simultaneously. Our main result is a new string index in the deterministic \emph{and} packed setting. Given a packed string $S$ of length $n$ over an alphabet $\sigma$, we show how to preprocess $S$ in $O(n)$ (deterministic) time and space $O(n)$ such that given a packed pattern string of length $m$ we can support queries in (deterministic) time $O\left(m/\alpha + \log m + \log \log \sigma\right), $ where $\alpha = w / \log \sigma$ is the number of characters packed in a word of size $w = \Theta(\log n)$. Our query time is always at least as good as the previous best known bounds and whenever several characters are packed in a word, i.e., $\log \sigma \ll w$, the query times are faster.