← 研踪 PaperTrailarXiv:2611.04753 · v1
Logarithmic Comparison-Query Complexity for EF1 Allocations
首次提交 2026-11-03 20:06
版本更新 2026-11-03 20:06
雷达观测 2026-11-04 23:39
摘要
We study the comparison-query complexity of computing allocations that are envy-free up to one item (EF1) for $n$ agents with heterogeneous additive preferences over $m$ indivisible items. In this model, the algorithm may only query which of two bundles an agent prefers, without ever observing numerical valuations or costs. Prior work established $O(\log m)$ query bounds for at most three agents, leaving open whether query complexity logarithmic in $m$ is achievable for every fixed $n \ge 4$. We resolve this open question in the affirmative: for every fixed $n\ge2$, we design algorithms that compute EF1 allocations using $O(\log m)$ comparison queries, matching the known $Ω(\log m)$ lower bound. Our results hold for both chores with nonnegative costs and goods with nonnegative valuations.
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v1 · 2026-11-03 20:06 · 最新观测版本
Logarithmic Comparison-Query Complexity for EF1 Allocations
We study the comparison-query complexity of computing allocations that are envy-free up to one item (EF1) for $n$ agents with heterogeneous additive preferences over $m$ indivisible items. In this model, the algorithm may only query which of two bundles an agent prefers, without ever observing numerical valuations or costs. Prior work established $O(\log m)$ query bounds for at most three agents, leaving open whether query complexity logarithmic in $m$ is achievable for every fixed $n \ge 4$. We resolve this open question in the affirmative: for every fixed $n\ge2$, we design algorithms that compute EF1 allocations using $O(\log m)$ comparison queries, matching the known $Ω(\log m)$ lower bound. Our results hold for both chores with nonnegative costs and goods with nonnegative valuations.
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