arXiv subjects

Arash Ashuri

Publications and source records attributed to Arash Ashuri.

5 recordsLinked to original sources

arXiv2026

A Simple Polynomial-Time EFX Repair for Cancelable Valuations

The leximin++ proof of Plaut and Roughgarden for agents with identical monotone valuations gives a natural EFX-repair procedure: starting from an arbitrary partition, repeatedly transfer an eligible item to a minimum-valued bundle. The procedure terminates, but the standard argument gives no polynomial bound on the number of transfers, even for additive valuations. We show that a single deterministic tie-breaking rule makes this repair procedure polynomial for the broader class of cancelable valuations. Fix an ordering of the items consistent with their singleton values and always transfer the highest-ranked eligible item. Consecutive transferred items strictly decrease in this ordering, and hence the algorithm performs at most $m$ transfers, where $m$ is the number of items. Moreover, the repair procedure does not decrease the minimum bundle value or increase the maximum bundle value. As an application, for every fixed $\varepsilon>0$, we compute in polynomial time an allocation of restricted additive chores that is simultaneously EFX, $(1+\varepsilon)$-MMS, and a $2$-approximation to the optimal social cost. This improves upon the previous polynomial-time $4/3$-MMS guarantee. Finally, we exhibit a monotone cancelable ordering on five items with no additive representation, showing that the extension beyond additivity is genuine.

cs.GT↗

arXiv2026

EFX Allocations Exist on Multi-Graphs

We study the fair allocation of indivisible goods among agents, with a focus on limiting envy. A central fairness notion is envy-freeness up to any good (EFX), which requires that any envy toward another agent vanishes after the removal of any single good from the latter's bundle. The existence of EFX allocations is considered a major open problem in fair division. So far, it has only been established in limited settings. Christodoulou et al. [2023] proved the existence of EFX allocations for graphical valuations. In this setting, the agents correspond to the nodes of an underlying graph, and the goods correspond to the edges, and any good has positive value only for the endpoints of the corresponding edge. Their proof crucially relies on the restriction that the graph is simple, meaning that for any pair of agents, there is at most one good that has value to both. For multigraph valuations, where multiple goods may be valued by the same pair of agents, only partial results are known. Amanatidis et al. [2024] and Kaviani et al. [2025] obtained 2/3 and sqrt(2)/2 approximations of EFX, respectively; Kaviani et al. [2024] established existence under restricted additive valuations; and Afshinmehr et al. [2025a] proved existence under the assumption that the shortest cycle containing non-parallel edges has length at least 4. In this paper, we resolve this open problem by proving the existence of EFX allocations for multigraph instances under cancelable valuations, a strict superclass of additive valuation functions. Our proof is algorithmic and computes such allocations in polynomial time when the valuation functions are cancelable. This work contributes to the small number of EFX existence results that apply to an arbitrary number of agents.

cs.GT↗

arXiv2025

EFX Allocations Exist on Triangle-Free Multi-Graphs

We study the fair allocation of indivisible goods among agents, with a focus on limiting envy. A central open question in this area is the existence of EFX allocations-allocations in which any envy of any agent i towards any agent j vanishes upon the removal of any single good from j's bundle. Establishing the existence of such allocations has proven notoriously difficult in general, but progress has been made for restricted valuation classes. Christodoulou et al. [2023] proved existence for graphical valuations, where goods correspond to edges in a graph, agents to nodes, and each agent values only incident edges. The graph was required to be simple, i.e., for any pair of agents, there could be at most one good that both agents value. The problem remained open, however, for multi-graph valuations, where for a pair of agents several goods may have value to both. In this setting, Sgouritsa and Sotiriou [2025] established existence whenever the shortest cycle with non-parallel edges has length at least six, while Afshinmehr et al. [2025] proved existence when the graph contains no odd cycles. In this paper, we strengthen these results by proving that EFX allocations always exist in multi-graphs that contain no cycle of length three. Assuming monotone valuations, we further provide a pseudo-polynomial time algorithm for computing such an allocation, which runs in polynomial time when agents have cancelable valuations, a strict superclass of additive valuation functions. Accordingly, our results stand as one of the only cases where EFX allocations exist for an arbitrary number of agents.

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arXiv2024

Simultaneously Satisfying MXS and EFL

The two standard fairness notions in the resource allocation literature are proportionality and envy-freeness. If there are n agents competing for the available resources, then proportionality requires that each agent receives at least a 1/n fraction of their total value for the set of resources. On the other hand, envy-freeness requires that each agent weakly prefers the resources allocated to them over those allocated to any other agent. Each of these notions has its own benefits, but it is well known that neither one of the two is always achievable when the resources being allocated are indivisible. As a result, a lot of work has focused on satisfying fairness notions that relax either proportionality or envy-freeness. In this paper, we focus on MXS (a relaxation of proportionality) and EFL (a relaxation of envy-freeness). Each of these notions was previously shown to be achievable on its own [Barman et al.,2018, Caragiannis et al., 2023], and our main result is an algorithm that computes allocations that simultaneously satisfy both, combining the benefits of approximate proportionality and approximate envy-freeness. In fact, we prove this for any instance involving agents with valuation functions that are restricted MMS-feasible, which are more general than additive valuations. Also, since every EFL allocation directly satisfies other well-studied fairness notions like EF1, 1/2-EFX, 1/2-GMMS, and 2/3-PMMS, and every MXS allocation satisfies 4/7-MMS, the allocations returned by our algorithm simultaneously satisfy a wide variety of fairness notions and are, therefore, universally fair [Amanatidis et al., 2020].

cs.GT↗

arXiv2024

EF2X Exists For Four Agents

We study the fair allocation of indivisible goods among a group of agents, aiming to limit the envy between any two agents. The central open problem in this literature, which has proven to be extremely challenging, is regarding the existence of an EFX allocation, i.e., an allocation such that any envy from some agent i toward another agent j would vanish if we were to remove any single good from the bundle allocated to j. When the agents' valuations are additive, which has been the main focus of prior works, Chaudhury et al. [2024] showed that an EFX allocation is guaranteed to exist for all instances involving up to three agents. Subsequently, Berger et al. [2022] extended this guarantee to nice-cancelable valuations and Akrami et al. [2023] to MMS-feasible valuations. However, the existence of EFX allocations for instances involving four agents remains open, even for additive valuations. We contribute to this literature by focusing on EF2X, a relaxation of EFX which requires that any envy toward some agent vanishes if any two of the goods allocated to that agent were to be removed. Our main result shows that EF2X allocations are guaranteed to exist for any instance with four agents, even for the class of cancelable valuations, which is more general than additive. Our proof is constructive, proposing an algorithm that computes such an allocation in pseudopolynomial time. Furthermore, for instances involving three agents we provide an algorithm that computes an EF2X allocation in polynomial time, in contrast to EFX, for which the fastest known algorithm for three agents is only pseudopolynomial.

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