Online Bottleneck Matching

  • Barbara M. Anthony
  • Christine Chung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)

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.

Keywords

Competitive Ratio Online Algorithm Match Problem Response Graph Primary Server 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. In: ACM Conference on Electronic Commerce, pp. 225–234 (2009)Google Scholar
  3. 3.
    Idury, R., Schaffer, A.: A better lower bound for on-line bottleneck matching (1992) (manuscript)Google Scholar
  4. 4.
    Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993); Preliminary version appeared in SODA, pp. 231–240 (1991)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    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) MathSciNetCrossRefGoogle Scholar
  6. 6.
    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) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    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)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    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) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    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) MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Barbara M. Anthony
    • 1
  • Christine Chung
    • 2
  1. 1.Math and Computer Science DepartmentSouthwestern UniversityGeorgetownUSA
  2. 2.Department of Computer ScienceConnecticut CollegeNew LondonUSA

Personalised recommendations