Journal of Combinatorial Optimization

, Volume 32, Issue 4, pp 1232–1253 | Cite as

Serve or skip: the power of rejection in online bottleneck matching



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 shown 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 (SoS) 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 \({{\textsc {Grin}}^*(t)}\). We show that the SoS model of resource augmentation analysis can essentially simulate the doubled-server-capacity model, and then examine the performance of GriNN(t) and \({\textsc {Grin}^*(t)}\).


Online algorithms Bottleneck matching Resource augmentation Approximation algorithms Matching 



A preliminary version of this work was published in the proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2014. We would like to thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.


  1. Anthony BM, Chung C (2014) Online bottleneck matching. J Comb Optim 27(1):100–114 (preliminary version appeared in COCOA, pp. 257–268, 2012)MathSciNetCrossRefMATHGoogle Scholar
  2. Chung C, Pruhs K, Uthaisombut P (2008) The online transportation problem: on the exponential boost of one extra server. In: LATIN, pp 228–239Google Scholar
  3. Devanur NR, Hayes TP (2009) 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 71–78Google Scholar
  4. Fernandes CG, Schouery RCS (2014) Second-price ad auctions with binary bids and markets with good competition. Theor Comput Sci 540–541:103–114MathSciNetCrossRefMATHGoogle Scholar
  5. Fuchs B, Hochstättler W, Kern W (2005) Online matching on a line. Theor Comput Sci 332(1–3):251–264MathSciNetCrossRefMATHGoogle Scholar
  6. Gabow HN, Tarjan RE (1988) Algorithms for two bottleneck optimization problems. J Algorithm 9(3):411–417MathSciNetCrossRefMATHGoogle Scholar
  7. Garfinkel RS (1971) An improved algorithm for the bottleneck assignment problem. Oper Res 19(7):1747–1751CrossRefMATHGoogle Scholar
  8. Goel G, Mehta A (2008) 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 982–991Google Scholar
  9. Goldberg AV, Hartline JD, Wright A (2001) Competitive auctions and digital goods. In: Proceedings of the 12th annual ACM-SIAM symposium on discrete algorithms, SODA ’01, pp 735–744Google Scholar
  10. Gu A, Gupta A, Kumar A (2013) 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. ACMGoogle Scholar
  11. Gupta A, Kumar A, Stein C (2014) Maintaining assignments online: Matching, scheduling, and flows. In: Proceedings of the 25th annual ACM-SIAM symposium on discrete algorithms, SODA 2014, pp 468–479Google Scholar
  12. Hartline JD, Roughgarden T (2009) Simple versus optimal mechanisms. In: ACM conference on electronic commerce, pp 225–234Google Scholar
  13. Idury R, Schaffer A (1992) A better lower bound for on-line bottleneck matching, manuscript.
  14. Kalyanasundaram B, Pruhs K (1993) Online weighted matching. J Algorithm 14(3):478–488 (preliminary version appeared in SODA, pp. 231–240, 1991)MathSciNetCrossRefMATHGoogle Scholar
  15. Kalyanasundaram B, Pruhs K (2000a) Speed is as powerful as clairvoyance. J ACM 47:617–643 (preliminary version appeared in FOCS, pp. 214–221, 1995)MathSciNetCrossRefMATHGoogle Scholar
  16. Kalyanasundaram B, Pruhs K (2000b) The online transportation problem. SIAM J Discret Math 13(3):370–383 (preliminary version appeared in ESA, pp 484–493, 1995)MathSciNetCrossRefMATHGoogle Scholar
  17. Kalyanasundaram B, Pruhs KR (2000c) An optimal deterministic algorithm for online b-matching. Theor Comput Sci 233(1):319–325MathSciNetCrossRefMATHGoogle Scholar
  18. Khuller S, Mitchell SG, Vazirani VV (1994) On-line algorithms for weighted bipartite matching and stable marriages. Theor Comput Sci 127:255–267MathSciNetCrossRefMATHGoogle Scholar
  19. Megow N, Skutella M, Verschae J, Wiese A (2012) The power of recourse for online MST and TSP. In: Proceedings of automata, languages, and programming—39th international colloquium, ICALP 2012, Part I, pp 689–700Google Scholar
  20. Mehta A, Saberi A, Vazirani U, Vazirani V (2007) Adwords and generalized online matching. J ACM 54(5):22:1–22:19Google Scholar
  21. Phillips CA, Stein C, Torng E, Wein J (2002) Optimal time-critical scheduling via resource augmentation. Algorithmica 32(2):163–200 (preliminary version appeared in STOC, pp 140–149, 1997)MathSciNetCrossRefMATHGoogle Scholar
  22. Roughgarden T, Tardos É (2002) How bad is selfish routing? J ACM 49(2):236–259 (preliminary version appeared in FOCS, pp 93–102, 2000)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematics and Computer Science DepartmentSouthwestern UniversityGeorgetownUSA
  2. 2.Department of Computer ScienceConnecticut CollegeNew LondonUSA

Personalised recommendations