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• W4244964340 abstract "This issue's SIGEST paper, Perfect Packing Theorems and the Average-Case Behavior of Optimal and Online Bin Packing, is taken from SIAM Journal on Discrete Mathematics (SIDMA). Bin packing is a classical NP-hard problem with many practical applications. Given a list of items of different sizes and a set of fixed-capacity bins, how can the items be packed into the bins with a minimal amount of waste? If a CD contains at most an hour of music, how many CDs will it take to record a large collection of musical numbers of different duration? If expensive wood is supplied in fixed-length boards, how many boards are needed to produce a specified array of different-sized shelves? How should data files of varying dimension be stored into fixed-size blocks on disk?The original version of this paper first appeared in volume 13 of SIDMA in 2000, with the title Bin Packing with Discrete Item Sizes, Part I: Perfect Packing Theorems and the Average Case Behavior of Optimal Packings and seven distinguished coauthors---E. G. Coffman, Jr., C. Courcoubetis, M. R. Garey, D. S. Johnson, P. W. Shor, R. R. Weber, and M. Yannakakis. The SIGEST paper is substantially different from its first incarnation, in large part because certain proofs in the original paper have been superseded by the authors' subsequent work on a new sum of squares algorithm, cited in the present paper; the authors have accordingly omitted the relevant sections from the original paper. In addition, the authors have expanded and updated their summary of the latest results for discrete distributions.The paper gives a readable and short introduction not just to the classical bin packing problem, but also to the mathematical differences that arise when the item sizes must be drawn from a finite set---the typical case in real-world applications---compared to the often-made assumption in theoretical contexts that the item sizes are chosen based on a continuous probability distribution. Combinatorial questions disappear in the limit of the continuous case---but is something lost in moving from discrete to continuous models? The answer is yes, for reasons explained and illustrated through analyzing online algorithms, in which items are assigned to bins in the order of their appearance in the item list.The concluding section of the paper, written mainly for the SIGEST version, presents a clear and complete survey of knowledge about average-case behavior of bin packing algorithms under discrete distributions, along with a characterization of the differences between results for continuous and discrete distributions. It also describes an array of challenging open problems.We are grateful to the authors for giving us an impressive and engrossing SIGEST paper." @default.
• W4244964340 created "2022-05-12" @default.
• W4244964340 date "2002-01-01" @default.
• W4244964340 modified "2023-09-26" @default.
• W4244964340 title "SIGEST" @default.
• W4244964340 doi "https://doi.org/10.1137/siread000044000001000093000001" @default.
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