We study the average case performance of the Best Fit algorithm for on-line bin packing under the distribution U(j, k}, in which the item sizes are uniformly distributed in the discrete range (1/k, 2/k,⋯, j/k}. Our main result is that, in the case j = k - 2, the expected waste for an infinite stream, of items remains bounded. This settles an open problem posed recently by Coffman et al . It is also the first result which involves a detailed analysis of the infinite rnulti-dimensional Markov chain underlying the algorithm.
|Original language||American English|
|Title of host publication||Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996|
|Publisher||Association for Computing Machinery|
|Number of pages||8|
|State||Published - 28 Jan 1996|
|Event||7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996 - Atlanta, United States|
Duration: 28 Jan 1996 → 30 Jan 1996
|Name||Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms|
|Conference||7th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1996|
|Period||28/01/96 → 30/01/96|
Bibliographical noteFunding Information:
t CNRS, Ecole Normale Superieure de Lyon, France. E-mail: kenyonQlip.ens-lyon.fr. Work done while this author was visiting UC Berkeley, partially supported by a NATO Fellowship. SFaculty of Computer Science, Technion, Haifa 32000, Israel. E-mail: rabaniQcs . technion .ac. il. Work done while this author was a postdoctoral fellow in the Department of Computer Science, University of Toronto. §C!omputer Science Division, University of California, Berkeley CA 94720-1776. Email: sinclairQcs.berkeley.edu. Supported by NSF grant CCR-9505448 and a UC Berkeley Faculty Research Grant.