Skip to main content

The Power of Rejection in Online Bottleneck Matching

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8881)

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 demonstrated 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 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 Grin* \((t)\). We show that the Serve-or-Skip model of resource augmentation analysis can essentially simulate the doubled-server-capacity model, and then characterize the performance of GriNN \((t)\) and Grin* \((t)\).

Keywords

  • Greedy Algorithm
  • Competitive Ratio
  • Online Algorithm
  • Free Pass
  • Bipartite Match

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-12691-3_30
  • Chapter length: 17 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-12691-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

References

  1. Anthony, B.M., Chung, C.: Online bottleneck matching. J. Comb. Optim. 27(1), 100–114 (2014)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. 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)

    CrossRef  Google Scholar 

  3. Devanur, N.R., Hayes, T.P.: The adwords problem: online keyword matching with budgeted bidders under random permutations. In: Proceedings of the 10th ACM Conference on Electronic Commerce, EC ’09, pp. 71–78 (2009). ISBN: 978-1-60558-458-4

    Google Scholar 

  4. Fernandes, C.G., Schouery, R.C.: Second-price ad auctions with binary bids and markets with good competition. Theor. Comput. Sci. 540–541, 103–114 (2014). ISSN: 0304–3975

    CrossRef  MathSciNet  Google Scholar 

  5. Fuchs, B., Hochstättler, W., et al.: Online matching on a line. Theor. Comput. Sci. 332(1–3), 251–264 (2005). ISSN: 0304–3975

    CrossRef  MATH  Google Scholar 

  6. Gabow, H.N., Tarjan, R.E.: Algorithms for two bottleneck optimization problems. J. Algorithms 9(3), 411–417 (1988)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. Garfinkel, R.S.: An improved algorithm for the bottleneck assignment problem. Oper. Res. 19(7), 1747–1751 (1971)

    CrossRef  MATH  Google Scholar 

  8. Goel, G., Mehta, A.: Online budgeted matching in random input models with applications to adwords. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’08, pp. 982–991 (2008)

    Google Scholar 

  9. Goldberg, A.V., Hartline, J.D., et al.: Competitive auctions and digital goods. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’01, pp. 735–744 (2001). ISBN: 0-89871-490-7

    Google Scholar 

  10. Gu, A., Gupta, A., et al.: The power of deferral: maintaining a constant-competitive Steiner tree online. In Proceedings of the 45th Annual ACM Symposium on Theory of Computing, pp. 525–534. ACM (2013)

    Google Scholar 

  11. Gupta, A., Kumar, A., et al.: Maintaining assignments online: matching, scheduling, and flows. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, pp. 468–479 (2014)

    Google Scholar 

  12. Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. In: ACM Conference on Electronic Commerce, pp. 225–234 (2009)

    Google Scholar 

  13. Idury, R., Schaffer, A.: A better lower bound for on-line bottleneck matching (manuscript, 1992)

    Google Scholar 

  14. Kalyanasundaram, B., Pruhs, K.: Online weighted matching. J. Algorithms 14(3), 478–488 (1993)

    CrossRef  MATH  MathSciNet  Google Scholar 

  15. Kalyanasundaram, B., Pruhs, K.: The online transportation problem. SIAM J. Discrete Math. 13(3), 370–383 (2000)

    CrossRef  MathSciNet  Google Scholar 

  16. Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47, 617–643 (2000). ISSN: 0004–5411

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Kalyanasundaram, B., Pruhs, K.R.: An optimal deterministic algorithm for online b-matching. Theor. Comput. Sci. 233(1), 319–325 (2000)

    CrossRef  MATH  MathSciNet  Google Scholar 

  18. Khuller, S., Mitchell, S.G., et al.: On-line algorithms for weighted bipartite matching and stable marriages. Theor. Comput. Sci. 127, 255–267 (1994). ISSN: 0304–3975

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. Megow, N., Skutella, M., Verschae, J., Wiese, A.: The power of recourse for online MST and TSP. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 689–700. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  20. Mehta, A., Saberi, A., et al.: Adwords and generalized online matching. J. ACM 54(5) (2007). ISSN: 0004–5411

    Google Scholar 

  21. Phillips, C.A., Stein, C., et al.: Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2), 163–200 (2002)

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christine Chung .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Anthony, B.M., Chung, C. (2014). The Power of Rejection in Online Bottleneck Matching. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12691-3_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)