$r$-indexing Wheeler graphs

TL;DR

This paper introduces a new indexing method for Wheeler graphs that enables efficient pattern matching and vertex reporting, leveraging the graph's run structure and path decomposition to optimize space and query time.

Contribution

It presents a novel $r$-indexing technique for Wheeler graphs that reduces storage to $O(r + 1)$ and supports fast pattern matching and vertex reporting.

Findings

Storage space is optimized to $O(r + 1)$.

Pattern matching runs in $O(|P| \, \log \log |G|)$ time.

Vertex reporting is achieved in $O(\log \log |G|)$ time per vertex.

Abstract

Let $G$ be a Wheeler graph and $r$ be the number of runs in a Burrows-Wheeler Transform of $G$, and suppose $G$ can be decomposed into $\upsilon$ edge-disjoint directed paths whose internal vertices each have in- and out-degree exactly 1. We show how to store $G$ in $O (r + \upsilon)$ space such that later, given a pattern $P$, in $O (|P| \log \log |G|)$ time we can count the vertices of $G$ reachable by directed paths labelled $P$, and then report those vertices in $O (\log \log |G|)$ time per vertex.