Stochastic Matching via Local Sparsification

2026-05-13

AI Summary

This work addresses the challenge in decentralized matching systems where limited local communication bandwidth prevents the transmission of full compatibility information, thereby degrading global matching performance. The authors propose a two-stage local sparsification framework: each agent compresses its compatible edge set to a fixed budget of $k$ edges, after which a central coordinator computes a global matching. The key innovation lies in a local edge selection strategy grounded in the expected fractional solution of the matching instance, which for the first time establishes a theoretical link between local information constraints and global approximation guarantees. A novel “spread” metric is introduced to characterize performance bounds. Combining tools from stochastic matching theory, graph sparsification, and fractional programming, the proposed algorithm enjoys rigorous theoretical guarantees. Experiments on New York City ride-pooling data and adversarial synthetic benchmarks show that the method achieves near-optimal matchings even under extremely low local budgets, significantly outperforming existing online baselines.

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.

Problem

• stochastic matching
• local sparsification
• communication bandwidth
• decentralized systems
• matching constraints

Innovation

• stochastic matching
• local sparsification
• communication-constrained optimization
• approximation ratio
• fractional solution