Serve or skip: the power of rejection in online bottleneck matching

We consider the online matching problem, where n server-vertices lie in a metric space and n request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. We focus on the egalitarian bottleneck objective, where the goal is to minimize the maximum distance between any request and its server. It has been demonstrated that while there are effective algorithms for the utilitarian objective (minimizing total cost) in the resource augmentation setting where the offline adversary has half the resources, these are not effective for the egalitarian objective. Thus, we propose a new Serve-or-Skip bicriteria analysis model, where the online algorithm may reject or skip up to a specified number of requests, and propose two greedy algorithms: GRINN(t) and GRIN∗(t). We show that the Serve-or-Skip model of resource augmentation analysis can essentially simulate the doubled-servercapacity model, and then examine the performance of GRINN(t) and GRIN∗(t).