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Ioannis Kakatelis

Publications and source records attributed to Ioannis Kakatelis.

2 recordsLinked to original sources
arXiv2026

Core stability recognition for minimum-cost spanning tree games: Parameterized perspective

Minimum-cost spanning tree game (MSTG) is a cooperative game played on an undirected edge-weighted graph $(G,w)$ representing the network, where each vertex corresponds to a player and each edge has an associated cost~$w$. A distinguished vertex $s \in V(G)$ represents the supply or source. For any coalition of players $S$, the characteristic cost function $c(S)$ is defined as the minimum cost of a spanning tree with respect to $w$, connecting exactly the vertices in $S \cup \{s\}$. In this paper we study the computational complexity of deciding core membership for MSTG. In general, deciding whether a given allocation is in the core is \textsf{coNP}-hard~(Faigle et al.,International Journal of Game Theory,1997). We study the core recognition problem under the name {\sc MSTG Core Non-Membership}. We extend the hardness to graphs which are very close to being planar. On the positive side, we present several algorithmic results within the framework of parameterized complexity. We show that {\sc MSTG Core Non-Membership} is fixed-parameter tractable when parameterized by the support size of the allocation. Turning into structural parameters of graphs, we show that the problem admits an FPT algorithm parameterized by treewidth and signed neighborhood diversity. Last but not least, we investigate kernelization. While in general graphs, under standard complexity-theoretical assumptions, {\sc MSTG Core Non-Membership} does not admit a polynomial kernel parameterized by the vertex cover number, we design a cubic kernel in planar graphs. Furthermore, in general graphs, we obtain quadratic kernel for signed neighborhood diversity and linear kernel for the parameter feedback edge number.

cs.GT↗
arXiv2026

Almost EFX in Hypergraphs

We study the existence of envy-free-up-to-any-good (EFX) allocations of indivisible goods among agents with heterogeneous monotone valuations. Christodoulou et al. (2023) introduced the (multi-hyper)graph setting, where agents and goods are represented by vertices and edges of a graph respectively, and only the endpoints of an edge may have non-zero marginal value for it. Our work simplifies and extends previous results of Kaviani et al. (Alireza Kaviani, Masoud Seddighin, Amir Mohammad Shahrezaei. Almost Envy-Free Allocation of Indivisible Goods: A Tale of Two Valuations. WINE 2024) in this domain. First, we provide a simpler construction of EF2X allocation for general monotone valuations in hypergraphs with girth at least 3. We extend our ideas when the multiplicity of each edge is 2 and show that an EF3X allocation always exists for additive valuations. Both results can be constructed in polynomial time. Regarding EFX approximations, we provide a simpler construction for $\frac{\sqrt{2}}{2}$-EFX allocations in hypergraphs of girth at least 3 under subadditive valuations. We push the state-of-the-art by establishing the existence of $\frac{2}{3}$-EFX allocations for additive valuations when the edge multiplicity is 2. Both of the latter results can be constructed in pseudo-polynomial time. By addressing these multi-hypergraph settings, our work contributes to the ongoing effort to resolve the existence of EFX in increasingly general and applicable domains.

cs.GT↗