Wheeler maps

TL;DR

This paper introduces Wheeler maps, a data structure generalizing Wheeler graphs, enabling efficient pattern matching and tag retrieval in texts, with applications in pangenomic read alignment.

Contribution

We propose Wheeler maps, a novel data structure that efficiently preprocesses texts and retrieves tags for pattern occurrences, improving pangenomic read alignment techniques.

Findings

Constructed Wheeler maps with space complexity O(g + r + t).

Achieved pattern preprocessing in O(m log n) time.

Retrieved distinct tags in optimal O(k) time.

Abstract

Motivated by challenges in pangenomic read alignment, we propose a generalization of Wheeler graphs that we call Wheeler maps. A Wheeler map stores a text $T[1..n]$ and an assignment of tags to the characters of $T$ such that we can preprocess a pattern $P[1..m]$ and then, given $i$ and $j$, quickly return all the distinct tags labeling the first characters of the occurrences of $P[i..j]$ in $T$. For the applications that most interest us, characters with long common contexts are likely to have the same tag, so we consider the number $t$ of runs in the list of tags sorted by their characters' positions in the Burrows-Wheeler Transform (BWT) of $T$. We show how, given a straight-line program with $g$ rules for $T$, we can build an $O(g + r + t)$-space Wheeler map, where $r$ is the number of runs in the BWT of $T$, with which we can preprocess a pattern $P[1..m]$ in $O(m \log n)$ time and then return the $k$ distinct tags for $P[i..j]$ in optimal $O(k)$ time for any given $i$ and $j$. We show various further results related to prioritizing the most frequent tags.