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

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## 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 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 shown 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 (SoS) 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 \({{\textsc {Grin}}^*(t)}\). We show that the SoS model of resource augmentation analysis can essentially simulate the doubled-server-capacity model, and then examine the performance of GriNN(*t*) and \({\textsc {Grin}^*(t)}\).

### Keywords

Online algorithms Bottleneck matching Resource augmentation Approximation algorithms Matching## Notes

### Acknowledgments

A preliminary version of this work was published in the proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2014. We would like to thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.

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