MEM-finding with run-length compressed strings

Paola Bonizzoni; Davide Cozzi; Travis Gagie; Younan Gao; Ragnar Groot Koerkamp

MEM-finding with run-length compressed strings

Data Structures and Algorithms 2026-08-02 v1

Authors: Paola Bonizzoni , Davide Cozzi , Travis Gagie , Younan Gao , Ragnar Groot Koerkamp

Abstract

We show how to store a text $T [1..n]$ consisting of $\rho_T$ runs in $O (\rho_T + \chi)$ space, where $\chi$ is the size of the smallest suffixient set for $T$ , such that when we are given a pattern $P [1..m]$ consisting of $\rho_P$ runs we can find the maximal exact matches (MEMs) of $P$ with respect to $T$ in $O (\rho_P \log m)$ time plus constant time for each edge we would fully or partially descend in the suffix tree for $T$ while finding those MEMs. We then adapt and optimize our result to finding set-maximal exact matches (SMEMs) of query haplotypes with respect to stored haplotype panels.

Cite

@article{arxiv.2608.01387,
  title  = {MEM-finding with run-length compressed strings},
  author = {Paola Bonizzoni and Davide Cozzi and Travis Gagie and Younan Gao and Ragnar Groot Koerkamp},
  journal= {arXiv preprint arXiv:2608.01387},
  year   = {2026}
}