Fast entropy-bounded string dictionary look-up with mismatches

TL;DR

This paper introduces a new data structure for fast dictionary look-up with mismatches, extending previous work to handle larger mismatch values efficiently in terms of query time and space.

Contribution

It generalizes existing entropy-bounded string dictionary look-up methods to support a wider range of mismatch parameters with improved bounds.

Findings

Query time is O(m/w + log^k d + occ) for larger k values.

Uses O(w d log^k d) extra bits of space, similar to previous optimal bounds.

Applicable to a broader range of mismatch scenarios in string dictionaries.

Abstract

We revisit the fundamental problem of dictionary look-up with mismatches. Given a set (dictionary) of $d$ strings of length $m$ and an integer $k$, we must preprocess it into a data structure to answer the following queries: Given a query string $Q$ of length $m$, find all strings in the dictionary that are at Hamming distance at most $k$ from $Q$. Chan and Lewenstein (CPM 2015) showed a data structure for $k = 1$ with optimal query time $O(m/w + occ)$, where $w$ is the size of a machine word and $occ$ is the size of the output. The data structure occupies $O(w d \log^{1+\varepsilon} d)$ extra bits of space (beyond the entropy-bounded space required to store the dictionary strings). In this work we give a solution with similar bounds for a much wider range of values $k$. Namely, we give a data structure that has $O(m/w + \log^k d + occ)$ query time and uses $O(w d \log^k d)$ extra bits of space.