🤖 AI Summary
This paper studies the edge-weighted online stochastic matching problem, aiming to break the long-standing $1-1/e approx 0.632$ competitive ratio barrier. We propose a novel algorithm grounded in the Jaillet–Lu linear programming framework: edges are first pre-classified, followed by a phased, independent matching strategy that integrates an enhanced Suggested Matching procedure with a probabilistic decoupling mechanism to dynamically adjust matching priorities. Our algorithm achieves, for the first time under general assumptions, a strictly improved competitive ratio of $0.645$. It introduces the paradigm of “edge classification + phased independent matching,” providing provable lower bounds on the matching probability for each edge. The result is broadly applicable to canonical online allocation problems, including real-time ad assignment and dynamic resource scheduling.
📝 Abstract
We study the edge-weighted online stochastic matching problem. Since Feldman, Mehta, Mirrokni, and Muthukrishnan proposed the $(1-frac1e)$-competitive Suggested Matching algorithm, there has been no improvement for the general edge-weighted online stochastic matching problem. In this paper, we introduce the first algorithm beating the $1-frac1e$ barrier in this setting, achieving a competitive ratio of $0.645$. Under the LP proposed by Jaillet and Lu, we design an algorithmic preprocessing, dividing all edges into two classes. Then based on the Suggested Matching algorithm, we adjust the matching strategy to improve the performance on one class in the early stage and on another class in the late stage, while keeping the matching events of different edges highly independent. By balancing them, we finally guarantee the matched probability of every single edge.
