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arXiv · 2606.16816

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

Kui-Wang Choi
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Abstract

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.

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Kui-Wang Choi. 2026-06-15. Verification of Stochastic Dominance Envy-Freeness in Time Proportional to Input Size. https://arxiv.org/abs/2606.16816

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