MONI can find k-MEMs
Igor Tatarnikov, Ardavan Shahrabi Farahani, Sana Kashgouli, Travis, Gagie

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 such that, given a pattern , we can quickly report the maximal substrings of that each occur in at least times. We first show how we can add bits to Rossi et al.'s recent MONI index, where is the number of runs in the Burrows-Wheeler Transform of , such that it supports such queries in time. We then show how, if we are given at construction time, we can reduce the query time to .
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