In modern data center networks, thousands of hosts contend for shared link capacity; the scale of these systems makes centralized scheduling impractical. This article models such scheduling as a bipartite matching problem under communication constraints: senders express interest in forming connections, and receivers respond using only locally available information. A class of single-round probabilistic matching algorithms is proposed, built on two key ideas: degree-biased sampling, in which senders use receiver degrees to inform their random selection, and random thinning, in which senders report only a random subset of their connections. Analytical performance guarantees are established for random graph models. In sparse regimes, degree-biased sampling yields a higher expected matching size than prior communication-constrained algorithms; in denser settings, a counterintuitive phenomenon emerges where deliberately restricting available connections through thinning increases the expected number of matches. Combining thinning to degree two with greedy selection produces an algorithm that requires no parameter tuning and, in packet-level simulations with production traffic traces, significantly extends the network stability region. Although motivated by data center network scheduling, the underlying framework of bipartite matching under local information constraints is portable to other resource allocation settings.

翻译：在现代数据中心网络中，数千台主机竞争共享链路容量，此类系统的规模使得集中式调度变得不切实际。本文将该调度问题建模为通信约束下的二分图匹配：发送方表达建立连接的意愿，接收方仅利用本地可用信息进行响应。本文提出了一类单轮概率匹配算法，其核心基于两个关键思想：度偏采样（发送方利用接收方度数指导随机选择）与随机稀疏化（发送方仅报告连接的随机子集）。针对随机图模型建立了理论性能保证。在稀疏场景下，度偏采样相比现有通信约束算法能获得更高的期望匹配规模；而在密集场景下，出现了一种反直觉现象：通过稀疏化主动限制可用连接反而会增加预期匹配数。将稀疏化至二阶与贪心选择相结合的算法无需参数调优，在使用生产环境流量痕迹的包级仿真中显著扩展了网络稳定区域。尽管源于数据中心网络调度，该基于局部信息约束的二分图匹配框架可迁移至其他资源分配场景。