Quotient-convergence of submodular setfunctions

In our paper Quotient-convergence of Submodular Setfunctions, we introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of bounded degree graphs, which analyzes graph sequences via neighborhood sampling, we address the challenge…

Inverse problems on multi-unit assignment valuations

Inverse and bilevel optimization problems play a central role in both theory and applications. These two classes are known to be closely related and thus have often been discussed together In a recent paper titled On the Complexity of Inverse Bivariate Multi-unit Assignment Valuation Problems, we consider inverse problems for multi-unit assignment valuations. Multi-unit assignment…

Decompositions of submodular functions

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they found applications in the theory of finitely additive measures, nonlinear integrals, and electric capacities. Recently, a number of connections between these two branches…

Two papers at ICALP

The research group will present two papers at ICALP! The first one, Problems on group-labeled matroid bases, studies a collection of problems on finding bases and common bases of matroids with restrictions on their labels. The other, Splitting-off in hypergraphs, introduces a splitting-off operation in hypergraphs and shows that there exists a local connectivity preserving…

REU 2024

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. For this year’s topics, see…