arXiv subjects

AmirMohammad Shahrezaei

Publications and source records attributed to AmirMohammad Shahrezaei.

3 recordsLinked to original sources

arXiv2025

Improved Maximin Share Guarantee for Additive Valuations

The maximin share ($\textsf{MMS}$) is the most prominent share-based fairness notion in the fair allocation of indivisible goods. Recent years have seen significant efforts to improve the approximation guarantees for $\textsf{MMS}$ for different valuation classes, particularly for additive valuations. For the additive setting, it has been shown that for some instances, no allocation can guarantee a factor better than $1-\tfrac{1}{n^4}$ of maximin share value to all agents. However, the best currently known algorithm achieves an approximation guarantee of $\tfrac{3}{4} + \tfrac{3}{3836}$ for $\textsf{MMS}$. In this work, we narrow this gap and improve the best-known approximation guarantee for $\textsf{MMS}$ to $\tfrac{10}{13}$.

cs.GT↗

arXiv2025

Improved Approximate EFX Guarantees for Multigraphs

In recent years, a new line of work in fair allocation has focused on EFX allocations for $(p, q)$-bounded valuations, where each good is relevant to at most $p$ agents, and any pair of agents share at most $q$ relevant goods. For the case $p = 2$ and $q = \infty$, such instances can be equivalently represented as multigraphs whose vertices are the agents and whose edges represent goods, each edge incident to exactly the one or two agents for whom the good is relevant. A recent result of \citet{amanatidis2024pushing} shows that for additive $(2,\infty)$ bounded valuations, a $(\nicefrac{2}{3})$-EFX allocation always exists. In this paper, we improve this bound by proving the existence of a $(\nicefrac{1}{\sqrt{2}})$-$\efx$ allocation for additive $(2,\infty)$-bounded valuations.

cs.GT↗

arXiv2024

Almost Envy-free Allocation of Indivisible Goods: A Tale of Two Valuations

The existence of $\textsf{EFX}$ allocations stands as one of the main challenges in discrete fair division.In this paper, we present symmetrical results on the existence of $\textsf{EFX}$ and its approximate variations for two distinct valuations: restricted additive valuations and $(p,q)$-bounded valuations introduced by Christodoulou \etal \cite{christodoulou2023fair}. In a $(p,q)$-bounded instance, each good has relevance for at most $p$ agents, and any pair of agents shares at most $q$ common relevant goods. We show that instances with $(\infty,1)$-bounded valuations admit $\textsf{EF2X}$ allocations and $\textsf{EFX}$ allocations with at most $\lfloor {n}/{2} \rfloor - 1$ discarded goods, mirroring results for the restricted additive setting \cite{akrami2022ef2x}. We also present ${({\sqrt{2}}/{2})\textsf{-EFX}}$ algorithms for both restricted additive and $(\infty,1)$-bounded subadditive settings. The symmetry of these results suggests these valuations share symmetric structures. Building on this, we propose an $\textsf{EFX}$ allocation for restricted additive valuations when $p=2$ and $q=\infty$. To achieve these results, we further develop the rank concept introduced by Farhadi \etal \cite{farhadi2021almost} and introduce several new concepts such as virtual value, rankpath, and root, which advance the overall understanding of $\textsf{EFX}$ allocations. In addition, we suggest an updating rule based on the virtual values which we believe will lead to broader and more generalized results on $\textsf{EFX}$.

cs.GT↗