Abstract
In this paper, we study the advice complexity of the online bin packing problem. In this well-studied setting, the online algorithm is supplemented with some additional information concerning the input. We improve upon both known upper and lower bounds of online algorithms for this problem. On the positive side, we first provide a relatively simple algorithm that achieves a competitive ratio arbitrarily close to 1.5, using constant-size advice. Our result implies that 16 bits of advice suffice to obtain a competitive ratio better than any online algorithm without advice, thus improving the previously known bound of \(O(\log (n))\) bits required to attain this performance. In addition, we introduce a more complex algorithm that still requires only constant-size advice, and which is below 1.5-competitive, namely has competitive ratio arbitrarily close to 1.47012. This is the currently best performance of any online bin packing algorithm with sublinear advice. On the negative side, we extend a construction due to Boyar et al. [10] so as to show that no online algorithm with sub-linear advice can be 7/6-competitive, which improves upon the known lower bound of 9/8.
S. Angelopoulos, C. Dürr, S. Kamali, M. Renault and A. Rosén—Research supported in part by project ANR-11-BS02-0015 “New Techniques in Online Computation–NeTOC”.
S. Kamali—Research supported by the France Canada Research Fund.
This is a preview of subscription content, log in via an institution to check access.
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
Adamaszek, A., Renault, M.P., Rosén, A., van Stee, R.: Reordering buffer management with advice. In: Kaklamanis, C., Pruhs, K. (eds.) WAOA 2013. LNCS, vol. 8447, pp. 132–143. Springer, Heidelberg (2014)
Ásgeirsson, E.I., Ayesta, U., Coffman, E.G., Etra, J., Momcilovic, P., Phillips, D.J., Vokhshoori, V., Wang, Z., Wolfe, J.: Closed on-line bin packing. Acta Cybernetica 15(3), 361–367 (2002)
Balogh, J., Békési, J., Galambos, G.: New lower bounds for certain classes of bin packing algorithms. Theoretical Computer Science 440–441, 1–13 (2012)
Böckenhauer, H., Hromkovic, J., Komm, D., Krug, S., Smula, J., Sprock, A.: The string guessing problem as a method to prove lower bounds on the advice complexity. Theoretical Computer Science 554, 95–108 (2014)
Böckenhauer, H., Komm, D., Královic, R., Rossmanith, P.: The online knapsack problem: Advice and randomization. Theoretical Computer Science 527, 61–72 (2014)
Böckenhauer, H.J., Komm, D., Královič, R., Královič, R.: On the advice complexity of the \(k\)-server problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 207–218. Springer, Heidelberg (2011)
Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: On the advice complexity of online problems. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 331–340. Springer, Heidelberg (2009)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)
Boyar, J., Kamali, S., Larsen, K.S., López-Ortiz, A.: On the list update problem with advice. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 210–221. Springer, Heidelberg (2014)
Boyar, J., Kamali, S., Larsen, K.S., López-Ortiz, A.: Online bin packing with advice. In: Proc. 31st Symp. on Theoretical Aspects of Computer Science (STACS), pp. 174–186 (2014)
Dobrev, S., Královič, R., Pardubská, D.: Measuring the problem-relevant information in input. RAIRO - Theoretical Informatics and Applications 43(3), 585–613 (2009)
Emek, Y., Fraigniaud, P., Korman, A., Rosén, A.: Online computation with advice. Theoretical Computer Science 412(24), 2642–2656 (2011)
Epstein, L., Levin, A.: On bin packing with conflicts. SIAM J. Optimization 19(3), 1270–1298 (2008)
Galambos, G., Woeginger, G.J.: Repacking helps in bounded space online bin packing. Computing 49, 329–338 (1993)
Gambosi, G., Postiglione, A., Talamo, M.: Algorithms for the relaxed online bin-packing model. SIAM J. Computing 30(5), 1532–1551 (2000)
Grove, E.F.: Online bin packing with lookahead. In: Proc. 6th Symp. on Discrete Algorithms (SODA), pp. 430–436 (1995)
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 J. Computing 3, 256–278 (1974)
Komm, D., Královič, R.: Advice complexity and barely random algorithms. RAIRO - Theoretical Informatics and Applications 45(2), 249–267 (2011)
Renault, M.P., Rosén, A.: On online algorithms with advice for the k-server problem. Theory of Computing Systems 56(1), 3–21 (2015)
Renault, M.P., Rosén, A., van Stee, R.: Online algorithms with advice for bin packing and scheduling problems. CoRR abs/1311.7589 (2013)
Seiden, S.S.: On the online bin packing problem. Journal of the ACM 49, 640–671 (2002)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Angelopoulos, S., Dürr, C., Kamali, S., Renault, M., Rosén, A. (2015). Online Bin Packing with Advice of Small Size. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-21840-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21839-7
Online ISBN: 978-3-319-21840-3
eBook Packages: Computer ScienceComputer Science (R0)