Abstract
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 by Coffman et al. [4]. It is also the first result which involves a detailed analysis of the infinite multidimensional Markov chain underlying the algorithm.
| Original language | English |
|---|---|
| Pages (from-to) | 218-235 |
| Number of pages | 18 |
| Journal | Journal of Algorithms |
| Volume | 27 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 1998 |
| Externally published | Yes |
Bibliographical note
Funding Information:³Supported by NSF Grant CCR-9505448 and a UC Berkeley Faculty Research Grant. E-mail: [email protected].
Funding Information:
We study the average case performance of the Best Fit algorithm for on-line bin packing under the distribution U j, k4, in which the item sizes are uniformly distributed in the discrete range 1rk,2rk,..., jrk4. Our main result is that, in the case j s k y 2, the expected waste for an infinite stream of items remains bounded. This settles an open problem posed by Coffman et al. w4x. It is also the first result which involves a detailed analysis of the infinite multidimensional Markov chain underlying the algorithm. Q 1998 Academic Press * Work done while the author was visiting UC Berkeley, partially supported by a NATO Fellowship. E-mail: [email protected].
Funding Information:
² Most of this work was done while the author was a postdoctoral fellow in the Department of Computer Science, University of Toronto. Work at the Technion supported in part by a David and Ruth Moskowitz Academic Lectureship award and by a grant from the Technion fund for the promotion of sponsored research. E-mail: [email protected].