Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure
Abstract
We generalize the polynomial-time solvability of -\textsc{Diverse Minimum s-t Cuts} (De Berg et al., ISAAC'23) to a wider class of combinatorial problems whose solution sets have a distributive lattice structure. We identify three structural conditions that, when met by a problem, ensure that a -sized multiset of maximally-diverse solutions -- measured by the sum of pairwise Hamming distances -- can be found in polynomial time. We apply this framework to obtain polynomial time algorithms for finding diverse minimum - cuts and diverse stable matchings. Moreover, we show that the framework extends to two other natural measures of diversity. Lastly, we present a simpler algorithmic framework for finding a largest set of pairwise disjoint solutions in problems that meet these structural conditions.
Cite
@article{arxiv.2504.02369,
title = {Finding Diverse Solutions in Combinatorial Problems with a Distributive Lattice Structure},
author = {Mark de Berg and Andrés López Martínez and Frits Spieksma},
journal= {arXiv preprint arXiv:2504.02369},
year = {2025}
}