Greedy algorithms and poset matroids

TL;DR

This paper extends the matroid-theoretic framework for greedy algorithms to poset matroids, enabling generalized algorithms like Kruskal's to operate on abstract simplicial complexes, broadening their applicability.

Contribution

It introduces a generalization of matroid theory to poset matroids and adapts greedy algorithms like Kruskal's to new combinatorial structures.

Findings

Generalization of matroid theory to poset matroids

Extension of Kruskal's algorithm to abstract simplicial complexes

Broader applicability of greedy algorithms in combinatorics

Abstract

We generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes.