Journal ArticleDOI
Probabilistic behaviour of optical bin-packing solutions
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In this article, the bin-packing problem is studied from a probabilistic view, and it is shown that, when the sizes of the n elements to be packed are drawn independently from a probability distribution, then the minimum number of bins necessary for the packing of these n elements is asymptotically proportional to n in three cases.About:
This article is published in Operations Research Letters.The article was published on 1984-08-01. It has received 12 citations till now. The article focuses on the topics: Bin packing problem & Almost surely.read more
Citations
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Journal ArticleDOI
Adaptive Resource Provisioning for the Cloud Using Online Bin Packing
TL;DR: This paper presents an approach that uses virtualization technology to allocate data center resources dynamically based on application demands and support green computing by optimizing the number of servers actively used.
Journal ArticleDOI
Heuristic methods and applications: A categorized survey
TL;DR: An extensive search of journal publications on heuristic methods and applications produced 442 articles published in 37 journals during the last sixteen years, with some interesting historical patterns and directions for future work revealed.
Proceedings ArticleDOI
A probabilistic analysis of multidimensional bin packing problems
TL;DR: Probabilistic analyses of two kinds of multidimensional bin packing problems: vector packing and rectangle packing are given and it is shown that the results can be extended to a wide class of distributions of the piece sizes.
Proceedings ArticleDOI
Bin packing with items uniformly distributed over intervals [a,b]
TL;DR: A lower bound on the asymptotic expected number of bins used in an optimum packing is determined, related to the dual of the linear programming problem corresponding to the bin packing problem, by providing simple packing strategies which achieve them.
Journal ArticleDOI
Asymptotic Methods in the Probabilistic Analysis of Sequencing and Packing Heuristics
TL;DR: In this article, the authors survey the methods that have been used to obtain formal probabilistic analyses of heuristics for makespan scheduling and one-dimensional bin packing and present many of the key results in these research areas.
References
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Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
Journal ArticleDOI
Approximation algorithms for combinatorial problems
TL;DR: For the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as n^@e, where n is the problem size and @e>0 depends on the algorithm.
Journal ArticleDOI
A stochastic model of bin-packing
TL;DR: The asymptotic expected bin occupancy is obtained for a simple on-line algorithm and convergence properties are presented so that, for a given set of pieces, this measure can be related to the expected number of bins required relative to an optimization rule.