Dynamic online matching with budget refills
Maria Cherifa (ENSAE Paris), Cl\'ement Calauz\`enes, Vianney Perchet (ENSAE Paris)

TL;DR
This paper investigates online bipartite matching with dynamic budget refills, analyzing the performance of greedy and balance algorithms in stochastic and adversarial settings, revealing conditions for optimality and potential improvements.
Contribution
It introduces a novel model of online matching with dynamic budget refills and analyzes algorithm performance, including convergence to ODE solutions and conditions for near-optimality.
Findings
Greedy matching size converges to an explicit ODE solution in stochastic Erdős-Rényi graphs.
Balance algorithm achieves near-optimal performance in adversarial settings with scarce refills.
Regular refills can improve algorithm performance beyond traditional bounds.
Abstract
Inspired by sequential budgeted allocation problems, we study the online matching problem with budget refills. In this context, we consider an online bipartite graph , where the nodes in are discovered sequentially and nodes in are known beforehand. Each is endowed with a budget that dynamically evolves over time. Unlike the canonical setting, in many applications, the budget can be refilled from time to time, which leads to a much richer dynamic that we consider here. Intuitively, adding extra budgets in seems to ease the matching task, and our results support this intuition. In fact, for the stochastic framework considered where we studied the matching size built by Greedy algorithm on an Erd\H{o}s-R{\'e}yni random graph, we showed that the matching size generated by Greedy converges with high probability to a solution of an…
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Taxonomy
TopicsAuction Theory and Applications · Mobile Agent-Based Network Management · Peer-to-Peer Network Technologies
