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Generalized Bin Packing Problems

Mauro Maria Baldi
2013 4OR  
same capacity the goal is to minimize the number of bins used The Variable Sized Bin Packing Problem (VSBPP) a set of items with given volumes must be loaded into bins with different capacities the goal  ...  , minimize the number of bins used) a set of constraints to satisfy (for instance, capacity constraints).  ...  bound of value 2 exists We showed that no worst-case ratio bound can be computed for FF and BF when applied to the OGBPP We studied improved variants of the FF and BF and we showed that the same conclusion  ... 
doi:10.1007/s10288-013-0252-1 fatcat:jm4exkszmbd5dpousebfhqqog4

Fast algorithms for bin packing

David S. Johnson
1974 Journal of computer and system sciences (Print)  
is as good as that of FIRST FIT under a large variety of restrictions on the input. let S(L) be the number of bins used in the packing resulting when S is applied to list L.  ...  Low-order polynomial time algorithms for near-optimal solutions to the problem of bin packing are studied.  ...  Meyer for their interest and suggestions, especially the former for extensive editing help, and an anonymous referee for providing the result given here as Theorem 5.6.  ... 
doi:10.1016/s0022-0000(74)80026-7 fatcat:ugmylu6nx5btpmu44r6xnx7y2e

Bin Packing with Queues

Devavrat Shah, John N. Tsitsiklis
2008 Journal of Applied Probability  
We study the best achievable performance (in terms of the average queue size and delay) in a stochastic and dynamic version of the bin-packing problem.  ...  At each time unit, a single unit-size bin is available and can receive any of the queued items, as long as their total size does not exceed 1.  ...  Acknowledgments The second author would like to acknowledge discussions with Dimitris Bertsimas on this problem, about fifteen years ago.  ... 
doi:10.1239/jap/1231340224 fatcat:lghb5rctpne67de7jyxbwzvxie

Bin Packing with Queues

Devavrat Shah, John N. Tsitsiklis
2008 Journal of Applied Probability  
We study the best achievable performance (in terms of the average queue size and delay) in a stochastic and dynamic version of the bin-packing problem.  ...  At each time unit, a single unit-size bin is available and can receive any of the queued items, as long as their total size does not exceed 1.  ...  Acknowledgements The second author would like to acknowledge discussions with Dimitris Bertsimas on this problem, about fifteen years ago.  ... 
doi:10.1017/s0021900200004885 fatcat:s6fj7gac6zdk5hzl7p742rxkp4

On-line Sequential Bin Packing

András György, Gábor Lugosi, György Ottucsák
2008 Annual Conference Computational Learning Theory  
We consider a sequential version of the classical bin packing problem in which items are received one by one.  ...  Before the size of the next item is revealed, the decision maker needs to decide whether the next item is packed in the currently open bin or the bin is closed and a new bin is opened.  ...  Introduction In the classical off-line bin packing problem, an algorithm receives items (also called pieces) x 1 , x 2 , . . . , x n ∈ (0, 1].  ... 
dblp:conf/colt/GyorgyLO08 fatcat:upcrk34djnb23li6lvs376kz5y

On-Line Sequential Bin Packing

András György, Gábor Lugosi, György Ottucsák
2010 Journal of machine learning research  
Before the size of the next item is revealed, the decision maker needs to decide whether the next item is packed in the currently open bin or the bin is closed and a new bin is opened.  ...  We consider a sequential version of the classical bin packing problem in which items are received one by one.  ...  In that paper we erroneously claimed that it was possible to construct a sequential on-line bin packing algorithm that has a small regret with respect to all constant-threshold experts for all possible  ... 
dblp:journals/jmlr/GyorgyLO10 fatcat:dcj7tzrwcfhchn7vejg7xeuujm

Variants of Classical One Dimensional Bin Packing * [chapter]

János Csirik, Csanád Imreh
2018 Handbook of Approximation Algorithms and Metaheuristics, Second Edition  
In Section 33.2, we survey the variant in which the number of items packed is maximized.  ...  In this problem the number of bins, m, is fixed and the goal is to pack a maximum number of pieces into the m bins. This problem was first proposed by Coffman et al.  ... 
doi:10.1201/9781351236423-29 fatcat:tc3luijzvvexzdereydpscncbe

A Constraint for Bin Packing [chapter]

Paul Shaw
2004 Lecture Notes in Computer Science  
We introduce a constraint for one-dimensional bin packing. This constraint uses propagation rules incorporating knapsack-based reasoning, as well as a lower bound on the number of bins needed.  ...  We also demonstrate that when coupled with a standard bin packing search strategy, our constraint can be a competitive alternative to established operations research bin packing algorithms.  ...  In Cdbf, to find the minimal number of bins, we solve a succession of decision problems starting with the maximum number of bins set to the simple lower bound L 1 .  ... 
doi:10.1007/978-3-540-30201-8_47 fatcat:lwsgqctatrgypivpbhxfrpelly

Cloud Storage and Online Bin Packing [chapter]

Doina Bein, Wolfgang Bein, Swathi Venigella
2011 Studies in Computational Intelligence  
The work here is related to "bin packing", a well studied problem in theoretical computer science. As an aside the thesis will survey some of the literature related to bin packing.  ...  Given an online sequence of storage requests and a cost associated with serving the request by allocating space on a certain server one seeks to select the minimum number of servers as to minimize total  ...  The maximum wasted space is maximal for type 1 bin, as they pack 1 per bin.  ... 
doi:10.1007/978-3-642-24013-3_7 fatcat:eetu6kuit5cklariowhl7v7piq

Bin packing with general cost structures [article]

Leah Epstein, Asaf Levin
2009 arXiv   pre-print
However, in GCBP, the cost of a bin is not 1 as in classic bin packing, but it is a non-decreasing and concave function of the number of items packed in it, where the cost of an empty bin is zero.  ...  In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins.  ...  A packing is fractional if items can be cut into pieces, where pieces of one item can possibly be packed in different bins.  ... 
arXiv:0906.5051v1 fatcat:qjwnqkj2avhctbd7w7n25z72pm

Bin packing with general cost structures

Leah Epstein, Asaf Levin
2010 Mathematical programming  
However, in GCBP, the cost of a bin is not 1 as in classic bin packing, but it is a non-decreasing and concave function of the number of items packed in it, where the cost of an empty bin is zero.  ...  In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins.  ...  A packing is fractional if items can be cut into pieces, where pieces of one item can possibly be packed in different bins.  ... 
doi:10.1007/s10107-010-0403-5 fatcat:rulb7joyjvfjroes5nhn4kw54u

The two-dimensional bin packing problem with variable bin sizes and costs

David Pisinger, Mikkel Sigurd
2005 Discrete Optimization  
The two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins.  ...  The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles.  ...  In its simplest form, the BPP may be formulated as: given n items with sizes w i ∈ [0, 1], i = {1, . . . , n}, and an infinite number of bins of size 1, find the smallest number of bins needed to pack  ... 
doi:10.1016/j.disopt.2005.01.002 fatcat:dps7zu5tdnca7p2e7axpcun47u

Optimization By Ant Colony Hybryde For The Bin-Packing Problem

Ben Mohamed Ahemed Mohamed, Yassine Adnan
2009 Zenodo  
The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins.  ...  This article treats the case of objects with a free orientation of 90Ôùª.  ...  TABLE I COMPARISON I OF THE NUMBER OF BINS TO PACK THE ITEM.  ... 
doi:10.5281/zenodo.1072140 fatcat:dlhsayhi4vhcpcdfapxnutm65u

Harmonic Algorithms for Packing d-dimensional Cuboids Into Bins [article]

Eklavya Sharma
2021 arXiv   pre-print
Our algorithms also work for the multiple-choice bin packing problem.  ...  In addition, we study the multiple-choice bin packing problem that generalizes the rotational case.  ...  In the dD bin packing problem (dBP), we have to compute a feasible packing of I (without rotating the items) into the minimum number of bins that are dD unit cubes.  ... 
arXiv:2011.10963v4 fatcat:yv5y6q6myvbudp7c6t5exs4n3e

Beating the Harmonic lower bound for online bin packing [article]

Sandy Heydrich, Rob van Stee
2018 arXiv   pre-print
In the online bin packing problem, items of sizes in (0,1] arrive online to be packed into bins of size 1. The goal is to minimize the number of used bins.  ...  In this paper, we present an online bin packing algorithm with asymptotic competitive ratio of 1.5813. This is the first improvement in fifteen years and reduces the gap to the lower bound by 15%.  ...  Acknowledgements We thank the anonymous referees for their useful comments, and Leah Epstein for interesting discussions.  ... 
arXiv:1511.00876v7 fatcat:zsdb2rszbjdfblozkfrj3cpjx4
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