On the sum-of-squares algorithm for bin packing

Csirik, János; Johnson, David S.; Kenyon, Claire; Orlin, James B.; Weber, Richard

doi:10.1145/335305.335331

Cited by 39 publications

(65 citation statements)

References 19 publications

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“…All but one are off-line algorithms. The exception is the Sum of Squares (SS) algorithm [7,8] which is designed as an on-line algorithm but used here as a deterministic off-line heuristic. All heuristics described here, are presented with each problem instance's items pre-sorted in descending order of size.…”

Section: Benchmarksmentioning

confidence: 99%

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Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model

Sim

Hart

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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Novel deterministic heuristics are generated using Single Node Genetic Programming for application to the One Dimensional Bin Packing Problem. First a single deterministic heuristic was evolved that minimised the total number of bins used when applied to a set of 685 training instances. Following this, a set of heuristics were evolved using a form of cooperative co-evolution that collectively minimise the number of bins used across the same set of problems. Results on an unseen test set comprising a further 685 problem instances show that the single evolved heuristic outperforms existing deterministic heuristics described in the literature. The collection of heuristics evolved by cooperative co-evolution outperforms any of the single heuristics, including the newly generated ones.

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Section: Benchmarksmentioning

confidence: 99%

“…• Sum of Squares (SS) [7,8] is an on-line bin packing heuristic which puts items into bins such as to minimise the number of bins with equal free space. It is included here as a deterministic off-line heuristic with items presented in descending order of size.…”

Section: Benchmarksmentioning

confidence: 99%

Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model

Sim

Hart

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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“…This allocation policy encourages a variety of sizes of unallocated regions. When the input comes from a discrete distribution, this algorithm has nearoptimal behavior [11,29].…”

Section: One-dimensional Reductionmentioning

confidence: 99%

Algorithmic support for commodity-based parallel computing systems.

Leung¹,

Bender

Bunde

et al. 2003

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Follows 3 AbstractThe Computational Plant or Cplant is a commodity-based distributedmemory supercomputer under development at Sandia National Laboratories. Distributed-memory supercomputers run many parallel programs simultaneously. Users submit their programs to a job queue. When a job is scheduled to run, it is assigned to a set of available processors. Job runtime depends not only on the number of processors but also on the particular set of processors assigned to it. Jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs.This report introduces new allocation strategies and performance metrics based on space-filling curves and one dimensional allocation strategies. These algorithms are general and simple. Preliminary simulations and Cplant experiments indicate that both space-filling curves and one-dimensional packing improve processor locality compared to the sorted free list strategy previously used on Cplant. These new allocation strategies are implemented in Release 2.0 of the Cplant System Software that was phased into the Cplant systems at Sandia by May 2002.Experimental results then demonstrated that the average number of communication hops between the processors allocated to a job strongly correlates with the job's completion time. This report also gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures.The associated clustering problem is as follows: Given n points in d , find k points that minimize their average pairwise L 1 distance. Exact and approximate algorithms are given for these optimization problems. One of these algorithms has been implemented on Cplant and will be included in Cplant System Software, Version 2.1, to be released. In more preliminary work, we suggest improvements to the scheduler separate from the allocator.

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“…[5], [6] for good reviews), it is different in two important respects: first, the model is substantially more general in that we have multiple pools of different "bins" (PMs) and, second, the "items" (VMs) leave the system after a random service time. The work on models that are close to ours is very recent (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Shadow-Routing Based Dynamic Algorithms for Virtual Machine Placement in a Network Cloud

Guo

Stolyar

Walid³

2018

IEEE Trans. Cloud Comput.

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Abstract-We consider a shadow routing based approach to the problem of real-time adaptive placement of virtual machines (VM) in large data centers (DC) within a network cloud. Such placement in particular has to respect vector packing constraints on the allocation of VMs to host physical machines (PM) within a DC, because each PM can potentially serve multiple VMs simultaneously. Shadow routing is attractive in that it allows a large variety of system objectives and/or constraints to be treated within a common framework (as long as the underlying optimization problem is convex). Perhaps even more attractive feature is that the corresponding algorithm is very simple to implement, it runs continuously, and adapts automatically to changes in the VM demand rates, changes in system parameters, etc., without the need to re-solve the underlying optimization problem "from scratch". In this paper we focus on the minmax-DC-load problem. Namely, we propose a combined VM-to-DC routing and VM-to-PM assignment algorithm, referred to as Shadow scheme, which minimizes the maximum of appropriately defined DC utilizations. We prove that the Shadow scheme is asymptotically optimal (as one of its parameters goes to 0). Simulation confirms good performance and high adaptivity of the algorithm. Favorable performance is also demonstrated in comparison with a baseline algorithm based on VMware implementation [7], [8]. We also propose a simplified -"more distributed" -version of the Shadow scheme, which performs almost as well in simulations.

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On the sum-of-squares algorithm for bin packing

Abstract: In this paper we present a theoretical analysis of the deterministic on-line Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants.

Cited by 39 publications

References 19 publications

Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model

Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model

Algorithmic support for commodity-based parallel computing systems.

Shadow-Routing Based Dynamic Algorithms for Virtual Machine Placement in a Network Cloud

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