Abstract
We discuss recent work on the subject of selfish bin packing. In these problems, items are packed into bins, such that each item wishes to minimize its own payoff. We survey the known results for a number of variants, focusing on worst-case Nash equilibria and other kinds of equilibria, and mentioning several results regarding issues of complexity and convergence to equilibria.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adar, R., Epstein, L.: Selfish bin packing with cardinality constraints. Theoretical Computer Science (to appear, 2013)
Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games and Economic Behavior 65(2), 289–317 (2009)
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)
Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games IV. Annals of Mathematics Study, vol. 40, pp. 287–324. Princeton University Press (1959)
Aumann, Y., Dombb, Y.: Pareto efficiency and approximate pareto efficiency in routing and load balancing games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 66–77. Springer, Heidelberg (2010)
Babel, L., Chen, B., Kellerer, H., Kotov, V.: Algorithms for on-line bin-packing problems with cardinality constraints. Discrete Applied Mathematics 143(1-3), 238–251 (2004)
Baker, B.S., Coffman Jr., E.G.: A tight asymptotic bound for Next-Fit-Decreasing bin-packing. SIAM Journal on Algebraic and Discrete Methods 2(2), 147–152 (1981)
Bansal, N., Caprara, A., Sviridenko, M.: A new approximation method for set covering problems, with applications to multidimensional bin packing. SIAM Journal on Computing 39(4), 1256–1278 (2009)
Bilò, V.: On the packing of selfish items. In: Proc. of the 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), 9 p. IEEE (2006)
Cao, Z., Yang, X.: Selfish bin covering. Theoretical Computer Science 412(50), 7049–7058 (2011)
Caprara, A.: Packing d-dimensional bins in d stages. Mathematics of Operations Research 33(1), 203–215 (2008)
Caprara, A., Kellerer, H., Pferschy, U.: Approximation schemes for ordered vector packing problems. Naval Research Logistics 50(1), 58–69 (2003)
Caprara, A., Pferschy, U.: Worst-case analysis of the subset sum algorithm for bin packing. Operetions Research Letters 32(2), 159–166 (2004)
Caprara, A., Pferschy, U.: Modified subset sum heuristics for bin packing. Information Processing Letters 96(1), 18–23 (2005)
Chekuri, C., Khanna, S.: On multidimensional packing problems. SIAM Journal on Computing 33(4), 837–851 (2004)
Chien, S., Sinclair, A.: Strong and Pareto price of anarchy in congestion games. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 279–291. Springer, Heidelberg (2009)
Coffman Jr., E.G., Csirik, J.: Performance guarantees for one-dimensional bin packing. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics, ch. 32, 18 p. Chapman & Hall/Crc (2007)
Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing: A survey. In: Hochbaum, D. (ed.) Approximation Algorithms. PWS Publishing Company (1997)
Csirik, J., Leung, J.Y.-T.: Variants of classical one-dimensional bin packing. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics, ch. 33, 13 p. Chapman & Hall/Crc (2007)
Csirik, J., Leung, J.Y.-T.: Variable-sized bin packing and bin covering. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics, ch. 34, 11 p. Chapman & Hall/Crc (2007)
Csirik, J., Woeginger, G.J.: On-line packing and covering problems. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms: The State of the Art, ch. 7, pp. 147–177. Springer (1998)
Czumaj, A., Vöcking, B.: Tight bounds for worst-case equilibria. ACM Transactions on Algorithms 3(1) (2007)
Dósa, G., Epstein, L.: Generalized selfish bin packing. CoRR, abs/1202.4080 (2012)
Dósa, G., Sgall, J.: First Fit bin packing: A tight analysis. In: Proc. of 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), pp. 538–549 (2013)
Dubey, P.: Inefficiency of Nash equilibria. Mathematics of Operations Research 11(1), 1–8 (1986)
Epstein, L.: Online bin packing with cardinality constraints. SIAM Journal on Discrete Mathematics 20(4), 1015–1030 (2006)
Epstein, L., Kleiman, E.: Selfish bin packing. Algorithmica 60(2), 368–394 (2011)
Epstein, L., Kleiman, E.: On the quality and complexity of Pareto equilibria in the job scheduling game. In: Proc. of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), pp. 525–532 (2011)
Epstein, L., Kleiman, E.: Vector packing and vector scheduling with selfish jobs and items. Work in progress (2013)
Epstein, L., Kleiman, E., Mestre, J.: Parametric packing of selfish items and the subset sum algorithm. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 67–78. Springer, Heidelberg (2009)
Epstein, L., Krumke, S.O., Levin, A., Sperber, H.: Selfish bin coloring. Journal of Combinatorial Optimization 22(4), 531–548 (2011)
Epstein, L., Levin, A.: AFPTAS results for common variants of bin packing: A new method for handling the small items. SIAM Journal on Optimization 20(6), 3121–3145 (2010)
Epstein, L., van Stee, R.: This side up! ACM Transactions on Algorithms 2(2), 228–243 (2006)
Epstein, L., van Stee, R.: Multidimensional packing problems. In: Gonzalez, T.F. (ed.) Handbook of Approximation Algorithms and Metaheuristics, ch. 35, 15 p. Chapman & Hall/Crc (2007)
Faigle, U., Kern, W.: On some approximately balanced combinatorial cooperative games. Mathematical Methods of Operations Research 38(2), 141–152 (1993)
Faigle, U., Kern, W.: Approximate core allocation for binpacking games. SIAM Journal on Discrete Mathematics 11(3), 387–399 (1998)
Fernandes, C.G., Ferreira, C.E., Miyazawa, F.K., Wakabayashi, Y.: Selfish square packing. Electronic Notes in Discrete Mathematics 37, 369–374 (2011)
Fernandez de la Vega, W., Lueker, G.S.: Bin packing can be solved within 1 + ε in linear time. Combinatorica 1(4), 349–355 (1981)
Fiat, A., Kaplan, H., Levy, M., Olonetsky, S.: Strong price of anarchy for machine load balancing. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 583–594. Springer, Heidelberg (2007)
Fisher, D.C.: Next-fit packs a list and its reverse into the same number of bins. Operations Research Letters 7(6), 291–293 (1988)
Garey, M.R., Graham, R.L., Johnson, D.S., Yao, A.C.-C.: Resource constrained scheduling as generalized bin packing. Journal of Combinatorial Theory Series A 21(3), 257–298 (1976)
Garey, M.R., Johnson, D.S.: A 71/60 theorem for bin packing. Journal of Complexity 1(1), 65–106 (1985)
Graham, R.L.: Bounds on multiprocessing anomalies and related packing algorithms. In: Proceedings of the 1972 Spring Joint Computer Conference, pp. 205–217 (1972)
Han, X., Dósa, G., Ting, H.-F., Ye, D., Zhang, Y.: A note on a selfish bin packing problem. Journal of Global Optimization (2012)
Holzman, R., Law-Yone, N.: Strong equilibrium in congestion games. Games and Economic Behavior 21(1-2), 85–101 (1997)
Ieong, S., McGrew, B., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: A simple class of congestion games. In: Proceedings of the 20th National Conference on Artificial Intelligence, pp. 489–494 (2005)
Johnson, D.S.: Near-optimal bin packing algorithms. PhD thesis. MIT, Cambridge (1973)
Johnson, D.S.: Fast algorithms for bin packing. Journal of Computer and System Sciences 8(3), 272–314 (1974)
Johnson, D.S., Demers, A.J., Ullman, J.D., Garey, M.R., Graham, R.L.: Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3(4), 299–325 (1974)
Karmarkar, N., Karp, R.M.: An efficient approximation scheme for the one-dimensional bin-packing problem. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science (FOCS 1982), pp. 312–320 (1982)
Kellerer, H., Pferschy, U.: Cardinality constrained bin-packing problems. Annals of Operations Research 92(1), 335–348 (1999)
Kern, W., Qiu, X.: Integrality gap analysis for bin packing games. Operations Research Letters 40(5), 360–363 (2012)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Krause, K.L., Shen, V.Y., Schwetman, H.D.: Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems. Journal of the ACM 22(4), 522–550 (1975)
Krause, K.L., Shen, V.Y., Schwetman, H.D.: Errata: “Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems”. Journal of the ACM 24(3), 527–527 (1977)
Lee, C.C., Lee, D.T.: A simple online bin packing algorithm. Journal of the ACM 32(3), 562–572 (1985)
Luc, D.T.: Pareto optimality. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds.) Pareto Optimality, Game Theory and Equilibria, pp. 481–515. Springer (2008)
Mavronicolas, M., Spirakis, P.G.: The price of selfish routing. Algorithmica 48(1), 91–126 (2007)
Miyazawa, F.K., Vignatti, A.L.: Convergence time to Nash equilibrium in selfish bin packing. Electronic Notes in Discrete Mathematics 35, 151–156 (2009)
Miyazawa, F.K., Vignatti, A.L.: Bounds on the convergence time of distributed selfish bin packing. International Journal of Foundations of Computer Science 22(3), 565–582 (2011)
Miyazawa, F.K., Wakabayashi, Y.: Approximation algorithms for the orthogonal z-oriented threedimensional packing problem. SIAM Journal on Computing 29(3), 1008–1029 (1999)
Nash, J.: Non-cooperative games. Annals of Mathematics 54(2), 286–295 (1951)
Roughgarden, T.: Selfish routing and the price of anarchy. MIT Press (2005)
Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Seiden, S.S.: On the online bin packing problem. Journal of the ACM 49(5), 640–671 (2002)
Simchi-Levi, D.: New worst-case results for the bin-packing problem. Naval Research Logistics 41(4), 579–585 (1994)
Rozenfeld, O., Tennenholtz, M.: Strong and correlated strong equilibria in monotone congestion games. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 74–86. Springer, Heidelberg (2006)
Ullman, J.D.: The performance of a memory allocation algorithm. Technical Report 100, Princeton University, Princeton, NJ (1971)
Woeginger, G.J.: There is no asymptotic PTAS for for two-dimensional vector packing. Information Processing Letters 64(6), 293–297 (1997)
Ye, D., Chen, J.: Non-cooperative games on multidimensional resource allocation. Future Generation Computer Systems 29(6), 1345–1352 (2013)
Yu, G., Zhang, G.: Bin packing of selfish items. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 446–453. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Epstein, L. (2013). Bin Packing Games with Selfish Items. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-40313-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40312-5
Online ISBN: 978-3-642-40313-2
eBook Packages: Computer ScienceComputer Science (R0)