Online Bottleneck Matching

We consider the online bottleneck matching problem, where k serververtices lie in a metric space and k request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. The goal is to minimize the maximum distance between any request and its server. Because no algorithm can have a competitive ratio better thanO(k) for this problem, we use resource augmentation analysis to examine the performance of three algorithms: the naive GREEDY algorithm, PERMUTATION, and BALANCE. We show that while the competitive ratio of GREEDY improves from exponential (when each serververtex has one server) to linear (when each server-vertex has two servers), the competitive ratio of PERMUTATION remains linear when an extra server is introduced at each server-vertex. The competitive ratio of BALANCE is also linear with an extra server at each server-vertex, even though it has been shown that an extra server makes it constant-competitive for the min-weight matching problem.