Dynamic Weighted Matching with Heterogeneous Arrival and Departure Rates

TL;DR

This paper introduces an online algorithm for dynamic heterogeneous matching with unannounced departures, achieving a constant competitive ratio and balancing immediate and delayed matching to optimize overall match value.

Contribution

It presents a novel online algorithm for dynamic weighted matching with heterogeneous arrival and departure rates, achieving a 1/8-competitive ratio in arbitrary graphs.

Findings

Algorithm is 1/8-competitive with optimal-in-hindsight policy.

Balances immediate and delayed matching to improve market efficiency.

Applicable to arbitrary weighted graphs with heterogeneous agent dynamics.

Abstract

We study a dynamic non-bipartite matching problem. There is a fixed set of agent types, and agents of a given type arrive and depart according to type-specific Poisson processes. Agent departures are not announced in advance. The value of a match is determined by the types of the matched agents. We present an online algorithm that is (1/8)-competitive with respect to the value of the optimal-in-hindsight policy, for arbitrary weighted graphs. Our algorithm treats agents heterogeneously, interpolating between immediate and delayed matching in order to thicken the market while still matching valuable agents opportunistically.