The Power of Rejection in Online Bottleneck Matching Barbara M. Anthony 1 and Christine Chung 2 1 Math and Computer Science Department, Southwestern University, Georgetown, TX, USA anthonyb@southwestern.edu 2 Department of Computer Science, Connecticut College, New London, CT, USA cchung@conncoll.edu Abstract. 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 immedi- ately be permanently assigned to a server-vertex. We focus on the egalitarian bot- tleneck objective, where the goal is to minimize the maximum distance between any request and its server. It has been demonstrated that while there are effec- tive 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: GRI NN(t ) and GRIN*(t ). We show that the Serve-or-Skip model of resource augmentation anal- ysis can essentially simulate the doubled-server-capacity model, and then charac- terize the performance of GRI NN(t ) and GRIN*(t ). 1 Introduction We consider the well-studied problem of minimum-cost bipartite matching in a metric space. We are given n established points in the metric space, s 1 , s 2 ,..., s n , referred to as servers, which form one side of the bipartition. Over time, the other n points, r 1 ,r 2 ,...,r n , appear in the metric space, and we refer to them as requests. We must permanently match or assign each request r i , for i = 1...n, to a server upon its arrival, without any knowledge of future request locations r i+1 ,...,r n . The standard objective for this problem has been to minimize the total cost of the final matching. Formally, if d (r , s) gives the cost or distance in the metric space from point r to point s, and we use μ (r i ) to denote the server matched to request r i in the matching μ , the standard goal is to find a matching μ ∗ = argmin μ n ∑ i=1 d (r i ,μ (r i )). In this work, however, we consider instead the objective of minimizing the maximum distance from any request to its assigned server. That is, we seek a matching μ ∗ = argmin μ max i=1...n d (r i ,μ (r i )). This objective is also known as the bottleneck objective, and we refer to this problem as the online minimum-bottleneck matching problem.