The end of 2025 has been very successful for the research group in terms of publications: several of our submitted papers have been accepted by leading journals, including JCTB, Combinatorica, and SIDMA. It has been a challenging period with a lot of hard work, but we are happy to share the good news that, thanks…
The multiple exchange property for matroid bases states that for any bases $A$ and $B$ of a matroid and any subset $X\subseteq A\setminus B$, there exists a subset $Y\subseteq B\setminus A$ such that both $A-X+Y$ and $B+X-Y$ are bases. This classical result has not only found applications in matroid theory, but also in the analysis…
The Matroid Secretary Problem is a central question in online optimization, modeling sequential decision-making under combinatorial constraints. Despite significant progress, the Matroid Secretary Conjecture — which asks whether every matroid admits a constant-competitive algorithm — remains open. In the paper Free-Order Secretary for Two-Sided Independence Systems, we introduce a bipartite graph framework that unifies and…
Finding a Steiner strongly $k$-arc-connected orientation is particularly relevant in network design and reliability, as it guarantees robust communication between a designated set of critical nodes. Király and Lau introduced a rooted variant, called the Steiner Rooted Orientation problem, where one is given an undirected graph on $n$ vertices, a root vertex, and a set…
Narayanan and Fujishige showed the existence of the principal partition sequence of a submodular function, a structure with numerous applications in areas such as clustering, fast algorithms, and approximation algorithms. In our recent paper $\{s,t\}$-Separating Principal Partition Sequence of Submodular Functions, motivated by two applications, we develop a theory of $\{s,t\}$-separating principal partition sequence of…