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Approximate algorithms for the knapsack problem on parallel computers

P.S. Gopalakrishnan, I.V. Ramakrishnan, L.N. Kanal
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
In this paper, we present an efficient parallel algorithm for hnding approximate solutions to the O-l knapsack problem.  ...  Computing an optimal solution to the knapsack problem is known to be NP-hard.  ...  ACKNOWLEDGMENT We thank the anonymous referee for considerably shortening the proof of Theorem 3.3. Several other suggestions by the referees helped improve the presentation of the material.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0890-5401(91)90063-8">doi:10.1016/0890-5401(91)90063-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/arsuif67wvahblhpomnm3hjtsu">fatcat:arsuif67wvahblhpomnm3hjtsu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190319155250/https://core.ac.uk/download/pdf/82254588.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/61/74/61742f23de62c06db5e6290e6eed864bf465cffb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0890-5401(91)90063-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Parallel Probabilistic Computations on a Cluster of Workstations [chapter]

A. Radenski, A. Vann, B. Norris
<span title="">1998</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ubikuqtgk5gsjplis3d6r2e6k4" style="color: black;">Advances in Parallel Computing</a> </i> &nbsp;
We use this generic algorithm to derive specific parallel algorithms for two discrete optimization problems: the knapsack problem and the traveling salesperson problem.  ...  Such a generic parallel algorithm can be glued together with domain-specific sequential algorithms in order to derive approximate parallel solutions for different intractable problems.  ...  We derive a parallel evolutionary algorithm for the knapsack problem from the generic master-server algorithm as follows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0927-5452(98)80011-7">doi:10.1016/s0927-5452(98)80011-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ciqc24ov5zg6hmbnj6odyty5pa">fatcat:ciqc24ov5zg6hmbnj6odyty5pa</a> </span>
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Page 2199 of Mathematical Reviews Vol. , Issue 2000c [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “In this paper, an approximation for four kinds of knapsack problems with multiple constraints is studied: the 0/1 multiple constraint knapsack problem (0/1 MCKP), the inte- ger multiple constraint  ...  Zhang, Yin [Zhang, Yin*] (PRC-BJ-C; Beijing) Approximation for knapsack problems with multiple constraints.  ... 
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Page 3440 of Mathematical Reviews Vol. , Issue 2004d [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
For large- scale problems of this type the author proposes a computational model of ¢-approximate algorithms.  ...  Summary: “A new parallel algorithm for the knapsack problem is proposed, in which the method of divide and conquer is adopted.  ... 
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Book announcements

<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
The Martello-Toth algorithm). Computational experiments (Elact algorithms. Approximate algorithms). Facets of the knapsack polytope. The multiplechoice knapsack problem.  ...  Chapter 30: Algorithms for Parallel Computers. Pointer jumping. CRCW algorithms versus EREW algorithms. Brent's theorem and work efficiency. Work-efficient parallel prefix computation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(92)90042-9">doi:10.1016/0166-218x(92)90042-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tmyols4labfmpb2xgcevnbkl6y">fatcat:tmyols4labfmpb2xgcevnbkl6y</a> </span>
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Page 6138 of Mathematical Reviews Vol. , Issue 88k [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This paper is a survey of the literature of the algorithms, both exact and approximate, for knapsack problems.  ...  Summary: “We propose a parallel branch and bound algorithm for the quadratic assignment problem; this algorithm has been imple- mented on an asychronous multiprocessor machine with shared memory (the Cray  ... 
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Page 2683 of Mathematical Reviews Vol. , Issue 2001D [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We first propose a new broadcasting algorithm on the hypercube multi- processor for the parallel GJ algorithm.  ...  , Hans [Kellerer, Hans*] (A-GRAZ-OR; Graz) A polynomial time approximation scheme for the multiple knapsack problem.  ... 
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Page 3874 of Mathematical Reviews Vol. , Issue 84i [page]

<span title="">1984</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We propose a parallel branch and bound algorithm, a parallel algorithm for the knapsack problem, algorithms for finding all vertices of a polyhedron and all extreme rays of a cone, and a direct algorithm  ...  There are indications, however, that most knapsack problems for which we know that there is one and only one solution may be solved fast by the use of the new algorithm.”  ... 
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Parallel Evolutionary Algorithms and High Dimensional Optimization Problems

Nadia Abd-Alsabour
<span title="">2018</span> <i title="International Academy Publishing (IAP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3uo3zcmrgvgspdzqe6w6sjoezq" style="color: black;">Journal of Computers</a> </i> &nbsp;
The high dimensionality of various optimization problems raises the requirement for developing new appropriate optimization algorithms.  ...  A good instance of these algorithms is parallel evolutionary algorithms that can viably exploit the capabilities of various structures of parallel machines.  ...  GAs are particularly suitable for parallel computing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17706/jcp.13.11.1265-1271">doi:10.17706/jcp.13.11.1265-1271</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/udhhuq7mcjfzbetcilexbmkewy">fatcat:udhhuq7mcjfzbetcilexbmkewy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200214220453/http://www.jcomputers.us/vol13/jcp1311-03.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/05/8d/058d7becee72abb68eaef97c72fa340d9af95aae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17706/jcp.13.11.1265-1271"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

A note on the performance of genetic algorithms on zero-one knapsack problems

V. Scott Gordon, A. P. Wim Böhm, Darrell Whitley
<span title="">1994</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uo6yx5jpgnf2zl7mkrumytd4ti" style="color: black;">Proceedings of the 1994 ACM symposium on Applied computing - SAC &#39;94</a> </i> &nbsp;
For large problems, branch-and-bound and depth-first methods outperform the genetic algorithms both for finding optimal solutions and for finding approximate solutions quickly.  ...  The short critical path for branch-and-bound indicates that this algorithm also has greater potential parallelism than the genetic algorithm.  ...  For the longer time periods, the estimates produced by the genetic algorithm were close to those shown in Table 2  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/326619.326696">doi:10.1145/326619.326696</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/sac/GordonBW94.html">dblp:conf/sac/GordonBW94</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4rixhiqsgfahrgsi6fwwtvvqa4">fatcat:4rixhiqsgfahrgsi6fwwtvvqa4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20051030092949/http://gaia.ecs.csus.edu:80/~gordonvs/papers/knapsackNote.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3c/ae/3caec31b08fb5a88e871931f864b42c415486199.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/326619.326696"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Hardness of Approximation for Knapsack Problems

Harry Buhrman, Bruno Loff, Leen Torenvliet
<span title="2014-06-15">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
Furthermore, we give a simple new algorithm for approximating knapsack and subset-sum, that can be adapted to work for small space, or in small parallel time.  ...  Hardness of approximation for Knapsack problems Buhrman, H.M.; Loff, B.F.L.; Torenvliet, L.  ...  Acknowledgments We thank Ulle Endriss for asking the question that led to this paper, as well as Karl Bringmann, Radu Curticapean, and Dominik Scheder for pointing out that the sparsification lemma would  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-014-9550-z">doi:10.1007/s00224-014-9550-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qwgirc5sifa6flvmb7imrkcmpi">fatcat:qwgirc5sifa6flvmb7imrkcmpi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922223017/https://pure.uva.nl/ws/files/1887095/156267_10.1007_s00224_014_9550_z.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4f/04/4f0443d21f0dbc861e76acc2798e82e285c699fd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-014-9550-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

EFFICIENT SCHEDULING OF DYNAMIC PROGRAMMING ALGORITHMS ON MULTICORE ARCHITECTURES

TAUSIF DIWAN, S. R. SATHE
<span title="">2017</span> <i title="Taylor&#39;s University"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3vxazte2xfh4vfhg6itjiodlsq" style="color: black;">Journal of Engineering Science and Technology</a> </i> &nbsp;
/1) knapsack and so on.  ...  Dynamic programming is one of the Berkley 13 dwarfs widely used for solving various combinatorial and optimization problems, including matrix chain multiplication, longest common subsequence, binary (0  ...  These comparisons of parallel dynamic programming on GPUs can be extended. Various CPU and GPU optimizations can also be studied in this series of work in the context of regular dynamic programming.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://doaj.org/article/d5791df93f3543ccbe7abcdb9abadaf3">doaj:d5791df93f3543ccbe7abcdb9abadaf3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kwd6uicdezdanduhwbxdtcytra">fatcat:kwd6uicdezdanduhwbxdtcytra</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171202050113/http://jestec.taylors.edu.my/Vol%2012%20issue%205%20May%202017/12_5_9.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c8/89/c889a2e30e4b3d9f5334e9bd04a2142dab08cb6f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Bi-Criteria Multiple Knapsack Problem with Grouped Items [article]

Francisco Castillo-Zunino, Pinar Keskinocak
<span title="2020-05-30">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We propose algorithms which guarantee that rewards are not less than the optimal solution, with a bound on exceeded knapsack capacities.  ...  The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities.  ...  A scalable parallel genetic algorithm for the generalized assignment problem. Parallel computing, 46:98-119, 2015. Silvano Martello and Paolo Toth.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.00322v1">arXiv:2006.00322v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jsv44yznefdizjkll3vozsbhw4">fatcat:jsv44yznefdizjkll3vozsbhw4</a> </span>
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A Parallel Heuristic Method for Optimizing a Real Life Problem (Agricultural Land Investment Problem)

Sagvan A. Saleh
<span title="2018-12-21">2018</span> <i title="Nawroz University"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cybouigbyrcklbtjnhaxfox6ei" style="color: black;">Academic Journal of Nawroz University</a> </i> &nbsp;
This paper proposed a parallel method for solving the Agricultural Land Investment Problem (ALIP), the problem that has an important impact on the agriculture issues.  ...  The proposed method based on principles of parallel computing and neighborhood search methods.  ...  ., 2002) , proposed exact and approximate algorithms for solving a variation of the knapsack problem that is disjunctively constrained knapsack problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25007/ajnu.v7n4a286">doi:10.25007/ajnu.v7n4a286</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zagg4igdzbe23kchmwioregp4e">fatcat:zagg4igdzbe23kchmwioregp4e</a> </span>
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Sequential and Parallel Implementation of GRASP for the 0-1 Multidimensional Knapsack Problem

Bianca de Almeida Dantas, Edson Norberto Cáceres
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cx3f4s3qmfe6bg4qvuy2cxezyu" style="color: black;">Procedia Computer Science</a> </i> &nbsp;
Among these alternatives, metaheuristics seem to be suitable on the search for approximate solutions for the problem.  ...  In this work we propose a sequential and a parallel implementation for the multidimensional knapsack problem using GRASP metaheuristic.  ...  Introduction The knapsack problem (KP) is one of the most known problems of combinatorial optimization.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.procs.2015.05.411">doi:10.1016/j.procs.2015.05.411</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mn5isjhc45gelm57top2f5zjpq">fatcat:mn5isjhc45gelm57top2f5zjpq</a> </span>
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