arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
arXiv:2406. 12413v3 Announce Type: replace-cross Abstract: We study the problem of allocating a set of indivisible goods to a set of agents with additive valuation functions, aiming to achieve approximate envy-freeness up to any good ($\alpha$-EFX).
arXiv:2607. 23367v1 Announce Type: cross Abstract: We study whether strictly positive marginal values restore the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) for indivisible goods.
The paper investigates the compatibility of envy-freeness and equitability in fair division, focusing on both indivisible goods and chores. It shows that the relaxed notions EF1+EQ1 may not exist even for normalized additive valuations, but provides an algorithm that finds an EF1+EQ1 allocation for up to seven agents with binary goods. For chores, the authors prove that a stronger EFX+EQX guarantee always exists, regardless of normalization, and they also explore cross-notion ex‑ante and ex‑post fairness guarantees.
arXiv:2608.24400v1 Announce Type: cross Abstract: We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed local...
arXiv:2607. 23310v1 Announce Type: cross Abstract: We study an online variant of discrete fair division under generalized assignment budget constraints.
arXiv:2601. 17944v2 Announce Type: replace-cross Abstract: We study repeated allocation of shared resources among agents with time-varying demands and capped linear utilities.
The paper introduces a path‑closed framework for realizing independence systems via zero‑cost choices of primary terminals in directed acyclic flow instances, extending the triangle mechanism to all finite loopless independence systems. It shows that such systems, including all finite simple graphs and hypergraph independence systems without singleton forbidden hyperedges, admit polynomial‑size realizations measured by the incidence size of minimal forbidden sets. The authors further specialize to odd cycles, deriving a rational family that yields a fractional cheap‑selection vector violating the odd‑cycle inequality and establishing an exact additive‑congestion threshold that approaches 1/2 for large cycles.
arXiv:2609. 03846v1 Announce Type: cross Abstract: We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW).
arXiv:2608.29097v1 Announce Type: cross Abstract: This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ ``centers'' from a metric space that fairly represe...
arXiv:2510.03899v3 Announce Type: replace-cross Abstract: Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the \emph...
arXiv:2608.29635v1 Announce Type: new Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
The paper investigates the maximum strong independent set problem in finite hypergraphs, where the goal is to find the largest vertex set that intersects each hyperedge in at most one vertex. It introduces an incidence-structural toolkit, proving exact reductions for dominance, incidence twins, and weight‑1 blocks, and derives closed‑form and low‑weight upper bounds. The authors also present puncturing and covering certificates that refine these bounds and analyze a layered greedy clustering algorithm driven by block weights and residual incidence, providing feasibility, maximality, conditional optimality, and incidence‑local complexity guarantees.