Stochastic Matching via Local Sparsification

• URL: http://arxiv.org/abs/2605.14195v1
• Date: Wed, 13 May 2026 23:25:15 GMT
• Title: Stochastic Matching via Local Sparsification
• Abstract summary: In real-time ride-hailing systems, the primary bottleneck is often local communication bandwidth rather than the timing of the match itself.<n>We formalize this challenge by introducing a two-stage local sparsification framework.<n>We show that near-optimal global matching is achievable even with highly constrained local budgets.
• Score: 12.632233732703758
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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