Advertisement

Buyback Problem - Approximate Matroid Intersection with Cancellation Costs

  • Ashwinkumar Badanidiyuru Varadaraja
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas decisions to accept bids may be canceled at a cost that is a fixed fraction of the bid value. Previous to our work, deterministic and randomized algorithms were known when the constraint is a matroid constraint. We extend this and give a deterministic algorithm for the case when the constraint is an intersection of k matroid constraints. We further prove a matching lower bound on the competitive ratio for this problem. This problem has applications to banner advertisement, semi-streaming, routing, load balancing and other problems where preemption or cancellation of previous allocations is allowed.

Keywords

Bipartite Graph Competitive Ratio Online Algorithm Graph Construction Free Disposal 
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.
    Adler, R., Azar, Y.: Beating the logarithmic lower bound: randomized preemptive disjoint paths and call control algorithms. In: SODA, pp. 1–10 (1999)Google Scholar
  2. 2.
    Ashwinkumar, B.V., Kleinberg, R.: Randomized online algorithms for the buyback problem. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 529–536. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Azar, Y., Blum, A., Mansour, Y.: Combining online algorithms for rejection and acceptance. In: SPAA, pp. 159–163 (2003)Google Scholar
  4. 4.
    Babaioff, M., Hartline, J.D., Kleinberg, R.: Selling ad campaigns: online algorithms with buyback. In: EC (2009)Google Scholar
  5. 5.
    Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: A knapsack secretary problem with applications. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 16–28. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: SODA, pp. 434–443 (2007)Google Scholar
  7. 7.
    Canetti, R., Irani, S.: Bounding the power of preemption in randomized scheduling. In: STOC, pp. 606–615 (1995)Google Scholar
  8. 8.
    Chawla, S., Hartline, J.D., Malec, D.L., Sivan, B.: Multi-parameter mechanism design and sequential posted pricing. In: STOC (2010)Google Scholar
  9. 9.
    Constantin, F., Feldman, J., Muthukrishnan, S., Pál, M.: An online mechanism for ad slot reservations with cancellations. In: SODA (2009)Google Scholar
  10. 10.
    Cormode, G., Muthukrishnan, S.: Space efficient mining of multigraph streams. In: PODS, pp. 271–282 (2005)Google Scholar
  11. 11.
    Sarma, A.D., Gollapudi, S., Panigrahy, R.: Estimating pagerank on graph streams. In: PODS, pp. 69–78 (2008)Google Scholar
  12. 12.
    Demetrescu, C., Finocchi, I., Ribichini, A.: Trading off space for passes in graph streaming problems. In: SODA, pp. 714–723 (2006)Google Scholar
  13. 13.
    Dynkin, E.B.: Optimal choice of the stopping moment of a Markov process. Dokl. Akad. Nauk SSSR 150, 238–240 (1963)MathSciNetGoogle Scholar
  14. 14.
    Epstein, L., Levin, A., Mestre, J., Segev, D.: Improved approximation guarantees for weighted matching in the semi-streaming model. In: STACS (2010)Google Scholar
  15. 15.
    Feige, U., Mirrokni, V.S., Vondrak, J.: Maximizing non-monotone submodular functions. In: FOCS, pp. 461–471 (2007)Google Scholar
  16. 16.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the streaming model: the value of space. In: SODA, pp. 745–754 (2005)Google Scholar
  17. 17.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: On graph problems in a semi-streaming model. Theor. Comput. Sci. 348, 207–216 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Feldman, J., Korula, N., Mirrokni, V., Muthukrishnan, S., Pál, M.: Online ad assignment with free disposal. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 374–385. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Garay, J.A., Gopal, I.S.: Call preemption in communication networks. In: IEEE INFOCOM, pp. 1043–1050 (1992)Google Scholar
  20. 20.
    Garay, J.A., Gopal, I.S., Kutten, S., Mansour, Y., Yung, M.: Efficient on-line call control algorithms. J. Algorithms 23(1), 180–194 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Hajiaghayi, M.T., Kleinberg, R., Sandholm, T.: Automated online mechanism design and prophet inequalities. In: AAAI (2007)Google Scholar
  22. 22.
    Halava, V., Harju, T., Hirvensalo, M.: Positivity of second order linear recurrent sequences. Discrete Appl. Math. 154(3), 447–451 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Jenkyns, T.A.: The efficacy of the greedy algorithm. In: Proc. of 7th South Eastern Conference on Combinatorics, Graph Theory and Computing, pp. 341–350 (1976)Google Scholar
  24. 24.
    Kleinberg, R.: A multiple-choice secretary algorithm with applications to online auctions. In: SODA, pp. 630–631 (2005)Google Scholar
  25. 25.
    Korte, B., Hausmann, D.: An analysis of the greedy heuristic for independence systems. Annals of Discrete Math. 2, 65–74 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Korula, N., Pál, M.: Algorithms for secretary problems on graphs and hypergraphs. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 508–520. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  27. 27.
    Lee, J., Mirrokni, V.S., Nagarajan, V., Sviridenko, M.: Non-monotone submodular maximization under matroid and knapsack constraints. In: STOC (2009)Google Scholar
  28. 28.
    McGregor, A.: Finding graph matchings in data streams. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX 2005 and RANDOM 2005. LNCS, vol. 3624, pp. 170–181. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  29. 29.
    Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions ii. In: Mathematical Programming Study, pp. 73–87 (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ashwinkumar Badanidiyuru Varadaraja
    • 1
  1. 1.Cornell UniversityIthacaUSA

Personalised recommendations