可复用资源在线分配的渐近最优竞争比
Asymptotically Optimal Competitive Ratio for Online Allocation of Reusable Resources
AI总结：
针对可复用资源在线分配问题，提出了达到最优(1-1/e)竞争比的新算法及无分布感知版本，通过引入资源复用潜力度量和新型不等式系统分析方法，推广了在线资源分配的原对偶分析框架。
摘要：
我们研究可复用资源的在线分配（匹配、预算分配和品类规划）问题：资源请求的对抗序列随时间逐步呈现，且任何已分配资源的使用/租用时长服从随机分布，该分布独立于各资源对应的使用分布。此前已知，相对于提前知晓全部请求序列的全知基准（clairvoyant benchmark），贪心算法的竞争比为0.5（Gong等人，2021）。\n我们提出一种新算法，当各资源的初始容量较大且使用分布已知时，对任意使用分布均可达到(1-1/e)的竞争比。这是该问题可实现的最优竞争比保证，即没有任何在线算法能获得更优的竞争比。我们还提出了一种无分布感知的在线算法，并证明其在特殊情形下可达到(1-1/e)的竞争比。\n我们算法的核心是一个新的度量指标，它通过在计算层面制造同一资源各相同单元之间的不对称性，来纳入每个资源的复用潜力。我们通过为一个新型不等式系统构造可行解来确立算法的性能保证，该系统可直接与全知基准对比，而非使用基准的线性规划（LP）松弛。我们的技术推广了在线资源分配的原对偶分析框架，可能具有更广泛的应用价值。
英文摘要：
We consider the problem of online allocation (matching, budgeted allocations, and assortments) of reusable resources where an adversarial sequence of resource requests is revealed over time and any allocated resource is used/rented for a stochastic duration drawn independently from a resource dependent usage distribution. Previously, it was known that a greedy algorithm is 0.5--competitive against the clairvoyant benchmark that knows the entire sequence of requests in advance (Gong et al. (2021)). We give a novel algorithm that is $(1-1/e)$--competitive for arbitrary usage distributions when the starting capacity of each resource is large and the usage distributions are known. This is the best achievable competitive ratio guarantee for the problem, i.e., no online algorithm can have better competitive ratio. We also give a distribution oblivious online algorithm and show that it is $(1-1/e)$--competitive in special cases. At the heart of our algorithms is a new quantity that factors in the potential of reusability for each resource by (computationally) creating an asymmetry between identical units of the resource. We establish the performance guarantee for our algorithms by constructing a feasible solution to a novel system of inequalities that allows direct comparison with the clairvoyant benchmark instead of a linear programming (LP) relaxation of the benchmark. Our technique generalizes the primal-dual analysis framework for online resource allocation and may be of broader interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
