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. 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chung, C., Pruhs, K., Uthaisombut, P.: The Online Transportation Problem: On the Exponential Boost of One Extra Server. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 228–239. Springer, Heidelberg (2008)
Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. In: ACM Conference on Electronic Commerce, pp. 225–234 (2009)
Idury, R., Schaffer, A.: A better lower bound for on-line bottleneck matching (1992) (manuscript)
Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993); Preliminary version appeared in SODA, pp. 231–240 (1991)
Kalyanasundaram, B., Pruhs, K.: The online transportation problem. SIAM J. Discrete Math. 13(3), 370–383 (2000); Preliminary version appeared in ESA, pp. 484–493 (1995)
Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47, 617–643 (2000); Preliminary version appeared in FOCS, pp. 214–221 (1995)
Khuller, S., Mitchell, S.G., Vazirani, V.V.: On-line algorithms for weighted bipartite matching and stable marriages. Theor. Comput. Sci. 127, 255–267 (1994)
Phillips, C.A., Stein, C., Torng, E., Wein, J.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2), 163–200 (2002); Preliminary version appeared in STOC, pp. 140–149 (1997)
Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002); Preliminary version appeared in STOC, pp. 140–149 (1997); Preliminary version appeared in FOCS, pp. 93–102 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anthony, B.M., Chung, C. (2012). Online Bottleneck Matching. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-31770-5_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31769-9
Online ISBN: 978-3-642-31770-5
eBook Packages: Computer ScienceComputer Science (R0)