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.
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References
Adler, R., Azar, Y.: Beating the logarithmic lower bound: randomized preemptive disjoint paths and call control algorithms. In: SODA, pp. 1–10 (1999)
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)
Azar, Y., Blum, A., Mansour, Y.: Combining online algorithms for rejection and acceptance. In: SPAA, pp. 159–163 (2003)
Babaioff, M., Hartline, J.D., Kleinberg, R.: Selling ad campaigns: online algorithms with buyback. In: EC (2009)
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)
Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: SODA, pp. 434–443 (2007)
Canetti, R., Irani, S.: Bounding the power of preemption in randomized scheduling. In: STOC, pp. 606–615 (1995)
Chawla, S., Hartline, J.D., Malec, D.L., Sivan, B.: Multi-parameter mechanism design and sequential posted pricing. In: STOC (2010)
Constantin, F., Feldman, J., Muthukrishnan, S., Pál, M.: An online mechanism for ad slot reservations with cancellations. In: SODA (2009)
Cormode, G., Muthukrishnan, S.: Space efficient mining of multigraph streams. In: PODS, pp. 271–282 (2005)
Sarma, A.D., Gollapudi, S., Panigrahy, R.: Estimating pagerank on graph streams. In: PODS, pp. 69–78 (2008)
Demetrescu, C., Finocchi, I., Ribichini, A.: Trading off space for passes in graph streaming problems. In: SODA, pp. 714–723 (2006)
Dynkin, E.B.: Optimal choice of the stopping moment of a Markov process. Dokl. Akad. Nauk SSSR 150, 238–240 (1963)
Epstein, L., Levin, A., Mestre, J., Segev, D.: Improved approximation guarantees for weighted matching in the semi-streaming model. In: STACS (2010)
Feige, U., Mirrokni, V.S., Vondrak, J.: Maximizing non-monotone submodular functions. In: FOCS, pp. 461–471 (2007)
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)
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)
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)
Garay, J.A., Gopal, I.S.: Call preemption in communication networks. In: IEEE INFOCOM, pp. 1043–1050 (1992)
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)
Hajiaghayi, M.T., Kleinberg, R., Sandholm, T.: Automated online mechanism design and prophet inequalities. In: AAAI (2007)
Halava, V., Harju, T., Hirvensalo, M.: Positivity of second order linear recurrent sequences. Discrete Appl. Math. 154(3), 447–451 (2006)
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)
Kleinberg, R.: A multiple-choice secretary algorithm with applications to online auctions. In: SODA, pp. 630–631 (2005)
Korte, B., Hausmann, D.: An analysis of the greedy heuristic for independence systems. Annals of Discrete Math. 2, 65–74 (1978)
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)
Lee, J., Mirrokni, V.S., Nagarajan, V., Sviridenko, M.: Non-monotone submodular maximization under matroid and knapsack constraints. In: STOC (2009)
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)
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)
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Badanidiyuru Varadaraja, A. (2011). Buyback Problem - Approximate Matroid Intersection with Cancellation Costs. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_32
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DOI: https://doi.org/10.1007/978-3-642-22006-7_32
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