MONI can find k-MEMs

TL;DR

This paper extends the MONI index to efficiently find maximal substrings of a pattern that occur at least k times in a text, with improved query times when k is known beforehand.

Contribution

It introduces a method to augment the MONI index with additional bits to support k-MEM queries, achieving faster query times when k is fixed.

Findings

Supports k-MEM queries in O(k m log n) time with added bits.

Reduces query time to O(m log n) when k is known at construction.

Extends the applicability of the MONI index for frequency-based substring queries.

Abstract

Suppose we are asked to index a text $T [0..n - 1]$ such that, given a pattern $P [0..m - 1]$, we can quickly report the maximal substrings of $P$ that each occur in $T$ at least $k$ times. We first show how we can add $O (r \log n)$ bits to Rossi et al.'s recent MONI index, where $r$ is the number of runs in the Burrows-Wheeler Transform of $T$, such that it supports such queries in $O (k m \log n)$ time. We then show how, if we are given $k$ at construction time, we can reduce the query time to $O (m \log n)$.