发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对次可加估值的在线组合分配问题，提出期望多项式时间的 (6+ε)-竞争算法，并恢复离线 (2+ε)-近似，利用对称性改进为 (60/11+ε)-竞争。
AI 中文摘要
针对具有次可加估值的在线组合分配问题，Correa 和 Cristi（STOC 2023）证明了存在一个 6-竞争的在线算法，改进了此前由 Dütting、Kesselheim 和 Lucier（FOCS 2020）给出的最优 O(log log m)-竞争在线算法，其中 m 是物品数量。然而，Correa 和 Cristi 的结果是存在性的，是否可以通过使用多项式次需求预言机查询的高效在线算法达到常数竞争比的问题仍然悬而未决。在这项工作中，我们对此给出肯定回答，为任意常数 ε > 0 给出了一个期望多项式时间的 (6 + ε)-竞争在线算法。我们的技术还恢复了离线设置下 Feige（STOC 2006）的 (2 + ε)-近似结果。最后，当买家的估值来自相同分布时，我们利用对称性获得了改进的 (60/11 + ε)-竞争算法。从问题的自然配置 LP 松弛出发，我们的主要技术贡献是一个递归的 Bundle Score Generator (BSG)，它通过为每个买家请求的物品分配相关分数来解决物品冲突。与 Correa 和 Cristi 证明其存在的 Random Score Generator 不同，我们的 BSG 可以在期望多项式时间内高效计算。此外，它满足一个随机占优性质，该性质足以恢复 Feige 的离线结果和 Correa 和 Cristi 的在线结果。
英文摘要
For the online combinatorial allocation problem with subadditive valuations, Correa and Cristi (STOC 2023) proved the existence of a $6$-competitive online algorithm, improving on the previous best $O(\log\!\log m)$-competitive online algorithm due to Dütting, Kesselheim, and Lucier (FOCS 2020), where $m$ is the number of items. However, Correa and Cristi's result is existential, and it was left open whether a constant competitive ratio is attainable via an efficient online algorithm that uses a polynomial number of demand oracle queries. In this work, we answer this affirmatively, giving an expected-polynomial-time $(6 + ε)$-competitive online algorithm for any constant $ε> 0$. Our techniques also recover, in the offline setting, the $(2 + ε)$-approximation result of Feige (STOC, 2006). Finally, when the buyers' valuations are drawn from identical distributions, we exploit symmetry to obtain an improved $(60/11+ε)$-competitive algorithm. Starting with the natural configuration LP relaxation for the problem, our main technical contribution is a recursive Bundle Score Generator (BSG) that resolves item conflicts by assigning correlated scores to the items requested by each buyer. Unlike the Random Score Generator whose existence is shown by Correa and Cristi, our BSG is efficiently computable in expected polynomial time. Moreover, it satisfies a stochastic dominance property that is sufficient to recover both Feige's offline result and Correa and Cristi's online result.
