arXiv subjects

Kui-Wang Choi

Publications and source records attributed to Kui-Wang Choi.

4 recordsLinked to original sources

arXiv2026

Temporal Fair Division of Indivisible Mixed Manna: Tractable Settings

We study temporal fair division of indivisible mixed manna. Items arrive over time and must be allocated irrevocably; an item may be a good for some agents, a chore for others, and neutral for the rest. We require the cumulative allocation after every round to be envy-free up to one item (TEF1). Although deciding whether a TEF1 allocation exists is NP-hard even for goods, we identify several tractable settings. First, with at most $k$ item types, an online cyclic rule guarantees EF$\lceil k/2\rceil$ after every item arrival. Thus, every instance with at most two types admits an online TEF1 allocation; moreover, when the numbers of agents and types are fixed, TEF1 existence can be decided in polynomial time. Second, under agreement after agent-specific scaling, provided that the scaling factors are known before arrivals begin, an online rule produces an allocation that is EF1 and Pareto optimal after every item arrival. Third, for a two-part arrival sequence with common rankings, we give a rule that is EF1 after every item arrival. Fourth, when the number of agents is fixed and values are bounded integers, we give an exact pseudo-polynomial algorithm for deciding TEF1 existence. Finally, for goods, every TEF1 allocation gives each agent at least $1/n$ of her maximin share after every round; this factor is tight even for identical valuations and two rounds. Deciding whether an exact temporal maximin-share allocation exists is NP-hard for both goods and chores, even with identical valuations, two agents, and two rounds.

cs.GT↗

arXiv2026

Temporal Fair Division of Indivisible Goods with Structured Constraints

This paper investigates temporal fair division, a setting where items are allocated over multiple rounds and agents require cumulative fairness over time. We focus on dynamic extensions of classic fairness notions: Temporal Envy-Freeness Up to Any Good (TEFX), its $\alpha$-TEFX approximation, and Temporal Maximin Share (TMMS). Because these strict fairness criteria are known to be generally impossible to satisfy, we analyze the model under constraints to map the boundary between what is possible and what is not. Our contribution systematically maps the structural boundaries of these temporal fairness notions. Our main technical result introduces a novel dynamic backtracking framework that achieves exact TEFX for Strong Binary Valuations. We prove, via a lexicographical potential function argument, that this bounded historical reallocation systematically resolves temporal envy cycles and terminates in finite time. Finally, we establish tight approximation ratios for $\alpha$-TEFX under identical valuations and bi-valued goods, alongside targeted impossibility results for TEFX and TMMS, demonstrating exactly where temporal fairness is mathematically unattainable, and properly contextualizing prior algorithms that only implicitly satisfied our newly defined TMMS metric.

cs.GT↗

arXiv2026

Verification of Stochastic Dominance Envy-Freeness in Time Proportional to Input Size

We present a time-optimal algorithm for verifying Stochastic Dominance Envy-Freeness (SD-EF) and its relaxation, SD-EF up to one good (SD-EF1), in the fair division of indivisible goods. By leveraging a single-pass prefix-dominance check per agent and lazy-initialization, we reduce the verification complexity from the previously known $\mathcal{O}(n^2m)$ by Aziz (2016) to $\mathcal{O}(nm)$. Given that the input preference matrix is of size $nm$, our algorithm is asymptotically optimal with respect to the input size.

cs.GT↗

arXiv2026

Temporal Fair Division of Indivisible Goods with Scheduling

We study temporal fair division, where agents receive goods over multiple rounds and cumulative fairness is required. We investigate Temporal Envy-Freeness Up to One Good (TEF1) and Up to Any Good (TEFX), its approximation $\alpha$-TEFX, and Temporal Maximin Share (TMMS). Motivated by known impossibilities in standard settings, we consider the model in various restricted settings and extend it by introducing scheduling. Our main contributions draw the boundary between possibility and impossibility. First, regarding temporal fair division without scheduling, we prove that while constant-factor $\alpha$-TEFX is impossible in general, a $1/2$-approximation is achievable for generalized binary valuations and identical days with two agents. Second, regarding temporal fair division with scheduling, we demonstrate that a scheduling buffer of size at least $n/2$ enables TEF1 for identical days. However, we establish that TEFX and TMMS remain largely impossible even with scheduling or restricted domains. These results highlight the inherent difficulty of strict temporal fairness and quantify the trade-offs required to achieve approximation guarantees.

cs.GT↗