发表机构
Leonard N. Stern School of Business, New York University; Georgia Institute of Technology; Qiuzhen College, Tsinghua University; Tsinghua University; Yau Mathematical Sciences Center; Beijing Institute of Mathematical Sciences and Applications（纽约大学莱昂纳德·N.斯特恩商学院; 佐治亚理工学院; 清华大学求真书院; 清华大学; 丘成桐数学科学中心; 北京数学科学与应用研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非平稳奖励下可复用容量的在线二分图匹配问题，提出两种BALANCE型算法，达到匹配下界的竞争比，实验验证其在奖励漂移下的稳健性与有限容量性能。
AI 中文摘要
我们研究具有可复用服务器容量和非平稳奖励的在线二分图匹配问题。作业按顺序到达，会显示兼容的服务器、奖励率和处理时长，且必须不可撤销地接受或拒绝。已接受的作业仅在其处理区间内占用一个单位的服务器容量，因此一次分配可能会取代未知的未来作业序列。现有保证通常由全局奖励范围校准，当奖励在长时间范围内漂移时，该范围可能变得任意大。我们转而施加局部有界奖励条件：在相关时间窗口内，可竞争同一服务器的作业的奖励率差异最多为δ倍。在该条件下，我们开发了两种具有时间感知机会成本损失的BALANCE型算法。TS-BAL最大化可行复用调度上的累积阻塞损失，达到竞争比2ln(δD)+O(lnln(δ∨D))；GR-BAL使用该损失的贪心松弛，达到ln(δD)+O(lnln(δ∨D))，其主项匹配下界ln(δD)。数值实验表明，该算法在显著的全局奖励漂移下表现稳健，且在有限容量下性能良好。
英文摘要
We study online bipartite matching with reusable server capacity and non-stationary rewards. Jobs arrive sequentially, reveal compatible servers, reward rates, and processing durations, and must be accepted or rejected irrevocably. An accepted job occupies one unit of server capacity only during its processing interval, so an assignment may displace an unknown sequence of future jobs. Existing guarantees are typically calibrated by a global reward range, which can become arbitrarily large when rewards drift over a long horizon. We instead impose a locally bounded reward condition: reward rates of jobs that can compete for the same server within a relevant time window differ by at most a factor $δ$. Under this condition, we develop two BALANCE-type algorithms with time-aware opportunity-cost losses. TS-BAL maximizes cumulative blocking losses over feasible reuse schedules and achieves a competitive ratio of $2\ln(δD)+\mathcal O(\ln\ln(δ\vee D))$. GR-BAL uses a greedy relaxation of this loss and achieves $\ln(δD)+\mathcal O(\ln\ln(δ\vee D))$, matching a lower bound of $\ln(δD)$ in the leading term. Numerical experiments demonstrate robust performance under substantial global reward drift and favorable finite-capacity performance.
