Abstract
In this paper we study a general bin packing game with an interest matrix, which is a generalization of all the currently known bin packing games. In this game, there are some items with positive sizes and identical bins with unit capacity as in the classical bin packing problem; additionally we are given an interest matrix with rational entries, whose element \(a_{ij}\) stands for how much item i likes item j. The payoff of item i is the sum of \({a_{ij}}\) over all items j in the same bin with item i, and each item wants to stay in a bin where it can fit and its payoff is maximized. We find that if the matrix is symmetric, a Nash Equilibrium (NE) always exists. However the Price of Anarchy (PoA) may be very large, therefore we consider several special cases and give bounds for PoA. We present some results for the asymmetric case, too. Moreover we introduce a new metric, called the Price of Harmony (PoH for short), which we think is more accurate to describe the quality of an NE in the new model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bilò, V.: On the packing of selfish items. In: Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS’06). IEEE (2006)
Coffman Jr., E.G., Csirik, J., Galambos, G., Martello, S., Vigo, D.: Bin packing approximation algorithms: survey and classification. In: Pardalos, P.M., Du, D.-Z., Graham, R.L. (eds.) Handbook of Combinatorial Optimization, pp. 455–531. Springer, New York (2013)
Dósa, G., Epstein, L.: Generalized selfish bin packing, arXiv:1202.4080, pp. 1–43 (2012)
Dósa, G., Epstein, L.: The convergence time for selfish bin packing. In: Lavi, R. (ed.) SAGT 2014, LNCS 8768. Springer, Heidelberg (2014)
Dósa, G., Sgall, J.: First Fit bin packing: a tight analysis. In: Portier, N. Wilke, T. (eds.) Proceedings of the 30th Symposium on the Theoretical Aspects of Computer Science (STACS 2013), pp. 538–549. Kiel, Germany (2013)
Dósa, G., Sgall, J.: Optimal analysis of Best Fit bin packing. In: Esparza, J. (ed.) ICALP 2014, Part I, LNCS 8572. Springer, Heidelberg (2014)
Epstein, L., Kleiman, E.: Selfish bin packing. Algorithmica 60(2), 368–394 (2011)
Garey, M.R., Johnson, D.S.: Computer and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Ma, R., Dósa, G., Han, X., Ting, H.-F., Ye, D., Zhang, Y.: A note on a selfish bin packing problem. J. Glob. Optim. 56(4), 1457–1462 (2013)
Nash, J.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)
Ullman, J. D.: The performance of a memory allocation algorithm. Technical Report 100. Princeton University, Princeton, NJ, (1971)
Yu, G., Zhang, G.: Bin packing of selfish items. In: The 4th International Workshop on Internet and Network Economics (WINE’08), pp. 446–453 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this submission was published in COCOON 2015.
Zhenbo Wang: Partially supported by NSFC No. 11371216.
Xin Han: Partially supported by NSFC(11571060), RGC(HKU716412E).
György Dósa: Partially supported by Széchenyi 2020 under the EFOP-3.6.1-16-2016-00015, and by the National Research, Development and Innovation Office NKFIH under the Grant SNN 116095.
Zsolt Tuza: Partially supported by the National Research, Development and Innovation Office NKFIH under the Grant SNN 116095.
Rights and permissions
About this article
Cite this article
Wang, Z., Han, X., Dósa, G. et al. A General Bin Packing Game: Interest Taken into Account. Algorithmica 80, 1534–1555 (2018). https://doi.org/10.1007/s00453-017-0361-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00453-017-0361-x