Online bottleneck matching

Barbara M. Anthony () and Christine Chung ()
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Barbara M. Anthony: Southwestern University
Christine Chung: Connecticut College

Journal of Combinatorial Optimization, 2014, vol. 27, issue 1, No 9, 100-114

Abstract: Abstract We consider the online bottleneck matching problem, where $$k$$ server-vertices 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 than $$O(k)$$ 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 server-vertex 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.

Keywords: Online algorithms; Bottleneck matching; Resource augmentation; Approximation algorithms; Matching (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-012-9581-9

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