The classic online stochastic matching problem typically requires immediate and irrevocable matching decisions. However, in many modern decentralized systems such as real-time ride-hailing and distributed cloud computing, the primary bottleneck is often local communication bandwidth rather than the timing of the match itself. We formalize this challenge by introducing a two-stage local sparsification framework. In this setting, arriving requests must prune their realized compatibility sets to a strict budget of $k$ edges before a central coordinator optimizes the global matching. This creates a "middle ground" between local information constraints and global optimization utility. We propose a local selection strategy, parametrized by a fractional solution of the expected instance. Theoretically, we quantify the approximation ratio as a function of the solution's {\em spread}. We prove that under sufficient spread, our sparsifier globally preserves the expected size of the maximum matching. Empirically, we demonstrate the robustness of our approach using the New York City ride-hailing datasets and adversarial synthetic benchmarks. Our results show that near-optimal global matching is achievable even with highly constrained local budgets, significantly outperforming standard online baselines.

翻译：经典的在线随机匹配问题通常要求即时且不可撤销的匹配决策。然而，在现代许多分布式系统（如实时网约车和分布式云计算）中，主要瓶颈往往是本地通信带宽，而非匹配本身的时机。我们通过引入一个两阶段局部稀疏化框架来形式化这一挑战。在该设置中，到达的请求必须在中央协调器优化全局匹配之前，将其实现的兼容集修剪至严格预算$k$条边。这创建了局部信息约束与全局优化效用之间的“中间地带”。我们提出了一种局部选择策略，该策略由期望实例的分数解参数化。理论上，我们将近似比量化为该解“扩散程度”的函数。我们证明，在充分扩散条件下，我们的稀疏化器能够全局保留最大匹配的期望大小。实证方面，我们使用纽约市网约车数据集和对抗性合成基准展示了我们方法的鲁棒性。我们的结果表明，即使在高度受限的局部预算下，也能实现接近最优的全局匹配，显著优于标准在线基线方法。