Lars Rohwedder

Tatiana Rocha Avila, Lars Rohwedder, Leo Wennmann

Recent concurrent work by Dupré la Tour and Fujii and by Hollender, Manurangsi, Meka, and Suksompong [ITCS'26] introduced a generalization of classical discrepancy theory to non-additive functions, motivated by applications in fair division. As many classical techniques from discrepancy theory seem to fail in this setting, including linear algebraic methods like the Beck-Fiala Theorem [Discrete Appl. Math '81], it remains widely open whether comparable non-additive bounds can be achieved. Towards a better understanding of non-additive discrepancy, we study coverage functions in a sparse setting comparable to the classical Beck-Fiala Theorem. Our setting generalizes the additive Beck-Fiala setting, rank functions of partition matroids, and edge coverage in graphs. More precisely, assuming each of the $n$ items covers only $t$ elements across all functions, we prove a constructive discrepancy bound that is polynomial in $t$, the number of colors $k$, and $\log n$.

Lars Rohwedder, Leander Schnaars

In the Graph Scheduling problem we schedule a given multiset of edges on discrete time steps, such that at each step the set of edges forms a matching. The goal is to minimize the sum of weighted group completion times, where a group is a set of edges and it completes when the last edge has been scheduled. Two popular variants of this problem are Coflow Scheduling and Data Migration. Our main result is extending a recent iterated rounding approach from Coflow Scheduling, roughly corresponding to the bipartite case, to the general Graph Scheduling problem. This yields an essentially tight $(2+ε)$-approximation for the asymptotic setting where OPT is assumed to be large. For this we rely on polyhedral techniques from general matching, namely odd-set inequalities, and graph theoretical results on edge colorings in multigraphs. The state-of-the-art approximation algorithm for Data Migration is a $(1 + ϕ)$-approximation that improves when OPT is small. Taking the best of this and our main result, we obtain an improvement of the approximation rate for Data Migration in any regime.

Étienne Bamas, Andreas Maggiori, Lars Rohwedder et al.

As power management has become a primary concern in modern data centers, computing resources are being scaled dynamically to minimize energy consumption. We initiate the study of a variant of the classic online speed scaling problem, in which machine learning predictions about the future can be integrated naturally. Inspired by recent work on learning-augmented online algorithms, we propose an algorithm which incorporates predictions in a black-box manner and outperforms any online algorithm if the accuracy is high, yet maintains provable guarantees if the prediction is very inaccurate. We provide both theoretical and experimental evidence to support our claims.