Abstract
The study of balls-into-bins processes or occupancy problems has a long history. These processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins process is to allocate a set of independent objects (tasks, jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to minimize the maximum load. In this paper, we analyze the maximum load for the chains-into-bins problem, which is defined as follows. There are n bins, and m objects to be allocated. Each object consists of balls connected into a chain of length ℓ, so that there are m ℓ balls in total. We assume the chains cannot be broken, and that the balls in one chain have to be allocated to ℓ consecutive bins. We allow each chain d independent and uniformly random bin choices for its starting position. The chain is allocated using the rule that the maximum load of any bin receiving a ball of that chain is minimized. We show that, for d ≥ 2 and m·ℓ= O(n), the maximum load is ((ln ln m)/ln d) + O(1) with probability \(1-\tilde O(1/m^{d-1})\).
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
Azar, Y., Broder, A.Z., Karlin, A.R., Upfal, E.: Balanced Allocations. SIAM J. Computing 29, 180–200 (1999)
Berenbrink, P., Czumaj, A., Steger, A., Vöcking, B.: Balanced Allocations: The Heavily Loaded Case. SIAM J. Computing 35, 1350–1385 (2006)
Englert, M.: Chains of Length Two into Bins. Manuscript, University of Aachen
Fekete, S., Köhler, E., Teich, J.: Optimal FPGA module placement with temporal precedence constraints. In: Proc. of the Conference on Design, Automation and Test in Europe (DATE 2001), pp. 658–667 (2001)
Kenthapadi, K., Panigrahy, R.: Balanced allocation on graphs. In: Proc. of 17th Annual Symposium on Discrete Algorithms (SODA 2006), pp. 434–443 (2006)
Knuth, D.E.: Sorting and Searching, 2nd edn. The Art of Computer Programming, vol. 3. Addison-Wesley, Reading (1998)
Mitzenmacher, M., Richa, A.W., Sitaraman, R.: The Power of Two Random Choices: A Survey of Techniques and Results. In: Handbook of Randomized Computing (2000)
Mitzenmacher, M., Prabhakar, B., Shah, D.: Load Balancing with Memory. In: Proc. of the 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2002), pp. 799–808 (2002)
Patterson, D.A., Gibson, G.A., Katz, R.H.: A Case for Redundant Arrays of Inexpensive Disks (RAID). In: Proc. of SIGMOD International Conference on Management of Data, pp. 109–116 (1988)
Sanders, P., Vöcking, B.: Tail Bounds And Expectations For Random Arc Allocation And Applications. Combinatorics, Probability & Computing 12(3) (2003)
Steiger, C., Walder, H., Platzner, M.: Operating Systems for Reconfigurable Embedded Platforms: Online Scheduling of Real-Time Tasks. IEEE Trans. Computers 53(11), 1393–1407 (2004)
Talwar, K., Wieder, U.: Balanced allocations: the weighted case. In: Proc. of the 39th Symposium on Theory of Computing (STOC), pp. 256–265 (2007)
Vöcking, B.: How Asymmetry Helps Load Balancing. J. ACM 50(4), 568–589 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Batu, T., Berenbrink, P., Cooper, C. (2011). Chains-into-Bins Processes. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-19222-7_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19221-0
Online ISBN: 978-3-642-19222-7
eBook Packages: Computer ScienceComputer Science (R0)