Central European Journal of Operations Research

, Volume 25, Issue 4, pp 953–966 | Cite as

Online algorithms with advice for the dual bin packing problem

Original Paper


This paper studies the problem of maximizing the number of items packed into n bins, known as the dual bin packing problem, in the advice per request model. In general, no online algorithm has a constant competitive ratio for this problem. An online algorithm with 1 bit of advice per request is shown to be 3/2-competitive. Next, for \(0< \varepsilon < 1{/}2\), an online algorithm with advice that is \((1/(1-\varepsilon ))\)-competitive and uses \({O}(1/\varepsilon )\) bits of advice per request is presented.


Online algorithms Online computation with advice Competitive analysis Dual bin packing Multiple knapsack problem 



I would like to thank Reza Dorrigiv for suggesting this as an interesting problem to study. Also, I would like to thank Reza Dorrigiv and Norbert Zeh for useful preliminary discussions and Adi Rosén for helpful comments.


  1. Adamaszek A, Renault MP, Rosén A, van Stee R (2013) Reordering buffer management with advice. In: Approximation and Online Algorithms—11th International Workshop, WAOA 2013, Sophia Antipolis, France, 5–6 September, 2013, Revised Selected Papers, pp 132–143Google Scholar
  2. Albers S, Hellwig M (2014) Online makespan minimization with parallel schedules. In: Algorithm Theory—SWAT 2014—14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, 2–4 July, 2014. Proceedings, pp 13–25Google Scholar
  3. Angelopoulos S, Dürr C, Kamali S, Renault MP, Rosén A (2015) Online bin packing with advice of small size. In: Algorithms and Data Structures—14th International Symposium, WADS 2015, Victoria, BC, Canada, 5–7 August, 2015. Proceedings, pp 40–53Google Scholar
  4. Azar Y, Boyar J, Epstein L, Favrholdt LM, Larsen KS, Nielsen MN (2002) Fair versus unrestricted bin packing. Algorithmica 34(2):181–196CrossRefGoogle Scholar
  5. Böckenhauer H, Komm D, Královic R, Rossmanith P (2014) The online knapsack problem: advice and randomization. Theor Comput Sci 527:61–72CrossRefGoogle Scholar
  6. Böckenhauer HJ, Komm D, Královic R, Královic R, Mömke T (2009) On the advice complexity of online problems. In: ISAAC, pp 331–340Google Scholar
  7. Borodin A, El-Yaniv R (1998) Online computation and competitive analysis. Cambridge University Press, New YorkGoogle Scholar
  8. Boyar J, Kamali S, Larsen KS, López-Ortiz A (2016) Online bin packing with advice. Algorithmica 74(1):507–527CrossRefGoogle Scholar
  9. Boyar J, Larsen KS, Nielsen MN (2001) The accommodating function: a generalization of the competitive ratio. SIAM J Comput 31(1):233–258CrossRefGoogle Scholar
  10. Coffman EG, Leung JYT, Ting DW (1978) Bin packing: maximizing the number of pieces packed. Acta Inf 9:263–271CrossRefGoogle Scholar
  11. Cygan M, Jez L, Sgall J (2016) Online knapsack revisited. Theory Comput Syst 58(1):153–190CrossRefGoogle Scholar
  12. Dorrigiv R, He M, Zeh N (2012) On the advice complexity of buffer management. In: ISAAC, pp 136–145Google Scholar
  13. Dorrigiv R, López-Ortiz A (2005) A survey of performance measures for on-line algorithms. SIGACT News 36(3):67–81CrossRefGoogle Scholar
  14. Emek Y, Fraigniaud P, Korman A, Rosén A (2011) Online computation with advice. Theor Comput Sci 412(24):2642–2656CrossRefGoogle Scholar
  15. Epstein L, Favrholdt LM (2003) On-line maximizing the number of items packed in variable-sized bins. Acta Cybern 16(1):57–66Google Scholar
  16. Feldman J, Mehta A, Mirrokni V, Muthukrishnan S (2009) Online stochastic matching: Beating 1–1/e. Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS ’09IEEE Computer Society, Washington, DC, USA, pp 117–126Google Scholar
  17. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman, New YorkGoogle Scholar
  18. Grove EF (1995) Online bin packing with lookahead. Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms, SODA ’95 Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pp 430–436Google Scholar
  19. Johnson D (1973) Near-optimal bin packing algorithms. Ph.D. thesis, MITGoogle Scholar
  20. Kellerer H (1999) A polynomial time approximation scheme for the multiple knapsack problem. In: RANDOM-APPROX, pp 51–62Google Scholar
  21. Kellerer H, Kotov V, Speranza MG, Tuza Z (1997) Semi on-line algorithms for the partition problem. Oper Res Lett 21(5):235–242CrossRefGoogle Scholar
  22. Kellerer H, Pferschy U, Pisinger D (2004) Knapsack problems. Springer, BerlinCrossRefGoogle Scholar
  23. Mahdian M, Yan Q (2011) Online bipartite matching with random arrivals: An approach based on strongly factor-revealing lps. Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing, STOC ’11ACM, New York, NY, USA, pp 597–606Google Scholar
  24. Renault MP, Rosén A (2015) On online algorithms with advice for the k-server problem. Theory Comput Syst 56(1):3–21CrossRefGoogle Scholar
  25. Renault MP, Rosén A, van Stee R (2015) Online algorithms with advice for bin packing and scheduling problems. Theor Comput Sci 600:155–170CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CNRS and Université Paris DiderotParisFrance

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