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Vector Bin Packing with Multiple-Choice [chapter]

Boaz Patt-Shamir, Dror Rawitz
2010 Lecture Notes in Computer Science  
We consider a variant of bin packing called multiple-choice vector bin packing.  ...  To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of  ...  Multiple-Choice Vector Bin Packing (mvbp). Instance: Same as for unweighted mmk, with the addition of T bin types, where each bin type t is characterized by a vector b t ∈ (R + ) D .  ... 
doi:10.1007/978-3-642-13731-0_24 fatcat:csh2ml57rjd5vdw7uqe3ay6kgq

Vector bin packing with multiple-choice

Boaz Patt-Shamir, Dror Rawitz
2012 Discrete Applied Mathematics  
To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack the largest number of (incarnations of)  ...  This extends previous results, in which each item has a single incarnation and there was only one bin type (vector bin packing).  ...  Multiple-Choice Vector Bin Packing (mvbp). Instance: Same as for unweighted mmk, with the addition of T bin types, where each bin type t is characterized by a vector b t ∈ (R + ) D .  ... 
doi:10.1016/j.dam.2012.02.020 fatcat:xb2axw2cxffqhgespaiwp2tufy

Multiple-choice Vector Bin Packing: Arc-flow Formulation with Graph Compression [article]

Filipe Brandão, João Pedro Pedroso
2013 arXiv   pre-print
The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints.  ...  The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have several incarnations.  ...  Conclusions We propose an arc-flow formulation with graph compression for solving multiple-choice vector bin packing problems.  ... 
arXiv:1312.3836v1 fatcat:tyfwzmmrsngujpswqmbxhj7djy

Vector repacking algorithms for power-aware computing

Mario E. Consuegra, Giri Narasimhan, Raju Rangaswami
2013 2013 International Green Computing Conference Proceedings  
Vector repacking, like vector packing, aims to pack a set of input vectors such that the number of bins used is minimized, but has the additional goal of minimizing the changes from the previous packing  ...  In this paper we experiment with practical algorithms for the vector repacking problem and its variants.  ...  Repack requires the choice of a (static) vector packing algorithm, which is then applied to obtain an initial packing of the items; in subsequent intervals it again uses a vector packing algorithm to decide  ... 
doi:10.1109/igcc.2013.6604490 dblp:conf/green/ConsuegraNR13 fatcat:nwj7xksdibev5fduuunzlebrkm

VPSolver 3: Multiple-choice Vector Packing Solver [article]

Filipe Brandão
2016 arXiv   pre-print
In this paper, we present the algorithm introduced in VPSolver 3.0.0 for building compressed arc-flow models for the multiple-choice vector packing problem.  ...  VPSolver is a vector packing solver based on an arc-flow formulation with graph compression.  ...  and compression algorithm for multiple-choice vector bin packing problems.  ... 
arXiv:1602.04876v1 fatcat:tfwwn3cgunclditmmmnehrabrq

Analyzing Real-Time Multimedia Content From Network Cameras Using CPUs and GPUs in the Cloud [article]

Ahmed S. Kaseb, Bo Fu, Anup Mohan, Yung-Hsiang Lu, Amy Reibman, George K. Thiruvathukal
2018 arXiv   pre-print
vector bin packing problem, and solving it using an existing algorithm.  ...  paper describes a cloud resource manager that solves this problem by estimating the resource requirements of executing analysis programs using CPU or GPU, formulating the resource allocation problem as a multiple-choice  ...  Multiple-Choice Vector Bin Packing To make the resource allocation decisions shown in Figure 2 , this paper formulates resource allocation as a multiple-choice three bin types (c) the optimal solution  ... 
arXiv:1802.08176v2 fatcat:u3u3at7zhfdi7cpigjzaz6hjqa

A Fast Scalable Heuristic for Bin Packing [article]

Srikrishnan Divakaran
2019 arXiv   pre-print
only a constant number of bin configurations with bounded unused space.  ...  In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering  ...  randomly chosen from e δ (L), and (iii) Construct min-packing δ (T ) using recurrence Equation (1) with the choice of vectors restricted to C.  ... 
arXiv:1904.12467v1 fatcat:kub7oxrezbeazhjhlywhgxwlc4

Online Multidimensional Packing Problems in the Random-Order Model

David Naori, Danny Raz, Michael Wagner
2019 International Symposium on Algorithms and Computation  
We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource  ...  ACM Subject Classification Theory of computation → Packing and covering problems; Theory of computation → Online algorithms  ...  Another interesting special case of VGAP is the Vector Multiple Knapsack Problem (VMKP), in which all bins are identical, and the packing options of each item are identical for all bins.  ... 
doi:10.4230/lipics.isaac.2019.10 dblp:conf/isaac/NaoriR19 fatcat:nynljwfm7rghbd4e6umutmkz44

Solving Packing Problems with Few Small Items Using Rainbow Matchings [article]

Max Bannach, Sebastian Berndt, Marten Maack, Matthias Mnich, Alexandra Lassota, Malin Rau, Malte Skambath
2020 arXiv   pre-print
Our main results are fixed-parameter algorithms for vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by k.  ...  An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering.  ...  · n O(1)time algorithms for the vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by the number k of small items.  ... 
arXiv:2007.02660v1 fatcat:62amiwdibzeuxe62okvfg26ggu

Resource ratio based virtual machine placement in heterogeneous cloud data centres

Saikishor Jangiti, Sriram E, Rohith Jayaraman, Harini Ramprasad, V S Shankar Sriram
2019 Sadhana (Bangalore)  
We study the case of a CDC hosting heterogeneous Physical Machines (PMs) as a variable size vector bin-packing problem.  ...  The proposed heuristic is compared with well-known heterogeneity aware FFD-DRR and BFD bin centric heuristics using a dataset with random instances of both VMs and PMs of heterogeneous configurations.  ...  Variable Size Vector Bin-Packing (VSVBP) problem The standard Bin-Packing Problem (BPP) is solved by packing a group of one-dimensional (1D) items into multiple 1D bins of equal capacity.  ... 
doi:10.1007/s12046-019-1215-9 fatcat:dznzey7d3barfd563h4gz56bvy

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.  ...  -Shamir and Rawitz gave an algorithm for multiple-choice vector bin packing having AAR O(log d) and a PTAS for multiple-choice vector knapsack [27].  ... 
arXiv:2011.10963v4 fatcat:yv5y6q6myvbudp7c6t5exs4n3e

A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach

Dorit S. Hochbaum, David B. Shmoys
1988 SIAM journal on computing (Print)  
This was a dramatic difference from previously known work on the more general problem with different processing speeds. Although much work had been done  ...  Suppose that we have a set of jobs J with independent processing times p,..., Pn that are to be executed on m nonidentical machines; these machines run at different speeds s, ,., s".  ...  By the choice of j, p,_ py, so the bin that contained j before the interchange remains truly feasibly packed after the swap.  ... 
doi:10.1137/0217033 fatcat:wqkbztxcrzfnnazt6srdof7bhm

The Power of Filling in Balanced Allocations [article]

Dimitrios Los, Thomas Sauerwald, John Sylvester
2022 arXiv   pre-print
It is well known that if m balls (jobs) are placed sequentially into n bins (servers) according to the One-Choice protocol - choose a single bin in each round and allocate one ball to it - then, for m  ...  We also prove that the Packing process is more sample-efficient than One-Choice, that is, it allocates on average more than one ball per sample.  ...  Other works which study perturbations on the probability vector are: allocations on hypergraphs [11] , balls-into-bins with correlated choices [25] ; or balls-into-bins with hash functions [3] .  ... 
arXiv:2204.04057v1 fatcat:vvjetvsjs5awrfhhoysedpxyee

Approximation schemes for generalized two-dimensional vector packing with application to data placement

Hadas Shachnai, Tami Tamir
2012 Journal of Discrete Algorithms  
Indeed, the special case where there is a single item in each color is the well-known twodimensional vector packing (2DVP) problem.  ...  For multiple bins, we develop a PTAS for a subclass of instances arising in the data placement problem.  ...  We reduce our problem to the binary 2-dimensional multiple choice knapsack (B2D-MCK) problem.  ... 
doi:10.1016/j.jda.2011.07.001 fatcat:otetzvx2jfdgdjc3zcvvkgmrkm

Efficient bulk insertion into a distributed ordered table

Adam Silberstein, Brian F. Cooper, Utkarsh Srivastava, Erik Vee, Ramana Yerneni, Raghu Ramakrishnan
2008 Proceedings of the 2008 ACM SIGMOD international conference on Management of data - SIGMOD '08  
We show that this problem is a variation of NP-hard bin-packing, reduce it to a problem of packing vectors, and then give a solution with provable approximation guarantees.  ...  Notice that although this is related to the multiple-choice knapsack problem, the bin-packing problem, and the general assignment problem, the vector-packing problem is distinct from all of these, and  ...  Vector packing, along with move behavior, necessitates a novel algorithm to find minimum bin size.  ... 
doi:10.1145/1376616.1376693 dblp:conf/sigmod/SilbersteinCSVYR08 fatcat:vyfv2v5urzbhfaqeptn5pwjjai
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