The aim of the REU, initiated by Miklós Abért, Péter Pál Pach and Dömötör Pálvölgyi in 2020, is to offer research opportunities to Hungarian math students during the summer. The participants are divided into smaller groups, and then they work together for one month on problems posed by senior researchers. This year, the Matroid Optimization…
Inverse optimization problems have long been the focus of research due to their wide applicability in both theory and practice. Since the pioneering work of Burton and Toint, countless of applications and extensions emerged. In a series of two papers, we give min-max characterizations and simple algorithms for inverse optimization problems under various objectives. In…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.when the goal is to decide if two common independent sets suffice or not. However, Davies and McDiarmid showed that if both matroids are strongly base orderable, then the…
Horn functions form a subclass of Boolean functions possessing interesting structural and computational properties. These functions play a fundamental role in algebra, artificial intelligence, combinatorics, computer science, database theory, and logic. In a recent paper titled Hypergraph Horn functions, we introduce the subclass of hypergraph Horn functions that generalizes matroids and equivalence relations. We provide…
A combinatorial market consists of a set of indivisible items and a set of agents, where each agent has a valuation function that specifies for each subset of items its value for the given agent. From an optimization point of view, the goal is usually to determine a pair of pricing and allocation of the…