Stochastic Matching via Local Sparsification

TL;DR

This paper introduces a two-stage local sparsification framework for online stochastic matching, balancing local communication constraints with global optimization, and demonstrates its effectiveness through theoretical analysis and empirical tests on NYC ride-hailing data.

Contribution

It formalizes a local sparsification approach for stochastic matching, providing theoretical guarantees and empirical validation under local information constraints.

Findings

The sparsifier preserves the expected maximum matching size under sufficient spread.

The approach outperforms standard online baselines on NYC ride-hailing data.

Theoretical approximation ratio depends on the spread of the fractional solution.

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.