Topic

# Bin

About: Bin is a research topic. Over the lifetime, 26193 publications have been published within this topic receiving 110549 citations.

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Rice University

^{1}TL;DR: In this article, a data-based procedure for choosing the bin width parameter is proposed, which assumes a Gaussian reference standard and requires only the sample size and an estimate of the standard deviation.

Abstract: SUMMARY In this paper the formula for the optimal histogram bin width is derived which asymptotically minimizes the integrated mean squared error. Monte Carlo methods are used to verify the usefulness of this formula for small samples. A data-based procedure for choosing the bin width parameter is proposed, which assumes a Gaussian reference standard and requires only the sample size and an estimate of the standard deviation. The sensitivity of the procedure is investigated using several probability models which violate the Gaussian assumption.

1,633 citations

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TL;DR: This work examines the performance of a number of simple algorithms which obtain “good” placements and shows that neither the first-fit nor the best-fit algorithm will ever use more than $\frac{17}{10}L^ * + 2$ bins.

Abstract: The following abstract problem models several practical problems in computer science and operations research: given a list L of real numbers between 0 and l, place the elements of L into a minimum number $L^ * $ of “bins” so that no bin contains numbers whose sum exceeds l. Motivated by the likelihood that an excessive amount of computation will be required by any algorithm which actually determines an optimal placement, we examine the performance of a number of simple algorithms which obtain “good” placements. The first-fit algorithm places each number, in succession, into the first bin in which it fits. The best-fit algorithm places each number, in succession, into the most nearly full bin in which it fits. We show that neither the first-fit nor the best-fit algorithm will ever use more than $\frac{17}{10}L^ * + 2$ bins. Furthermore, we outline a proof that, if L is in decreasing order, then neither algorithm will use more than $\frac{11}{9} L^ * + 4$ bins. Examples are given to show that both upper bou...

930 citations

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TL;DR: Efficient approximation algorithms are devised, their limitations are studied, and worst-case bounds on the performance of the packings they produce are derived.

Abstract: We consider problems of packing an arbitrary collection of rectangular pieces into an open-ended, rectangular bin so as to minimize the height achieved by any piece. This problem has numerous applications in operations research and studies of computer operation. We devise efficient approximation algorithms, study their limitations, and derive worst-case bounds on the performance of the packings they produce.

676 citations

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TL;DR: An exact algorithm for filling a single bin is developed, leading to the definition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms.

Abstract: The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. The problem is strongly NP-hard and extremely difficult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotic worst-case performance ratio of the continuous lower bound is ?. An exact algorithm for filling a single bin is developed, leading to the definition of an exact branch-and-bound algorithm for the three-dimensional bin packing problem, which also incorporates original approximation algorithms. Extensive computational results, involving instances with up to 90 items, are presented: It is shown that many instances can be solved to optimality within a reasonable time limit.

569 citations