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General Knapsack Problems in a Dynamic Setting [article]

Yaron Fairstein, Ariel Kulik, Joseph Naor, Danny Raz
2021 arXiv   pre-print
In this paper we consider the Generalized Multistage d-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the d-Dimensional Knapsack problem.  ...  We present a PTAS for Generalized Multistage d-Knapsack.  ...  APPROX/RANDOM 2021 15:20 General Knapsack Problems in a Dynamic Setting We define the solution (S t , A t ) T t=1 for Q.  ... 
arXiv:2105.00882v2 fatcat:7mvu7o5am5dobe4pstnokb75ma

General Knapsack Problems in a Dynamic Setting

Yaron Fairstein, Ariel Kulik, Naor, Joseph (Seffi), Danny Raz, Mary Wootters, Laura Sanità
In this paper we consider the Generalized Multistage d-Knapsack problem, a generalization of the multistage variants of the Multiple Knapsack problem, as well as the d-Dimensional Knapsack problem.  ...  We present a PTAS for Generalized Multistage d-Knapsack.  ...  Subsequently, in Section 2.2 we show how the algorithm for bounded time horizon can be used to approximate general instance. 15:6 General Knapsack Problems in a Dynamic Setting Bounded Time Horizon  ... 
doi:10.4230/lipics.approx/random.2021.15 fatcat:gpm4g3lkmzg73pnltxuftxhkcy

Algorithms for the bounded set-up knapsack problem

Laura A. McLay, Sheldon H. Jacobson
2007 Discrete Optimization  
The Bounded Set-up Knapsack Problem (BSKP) is a generalization of the Bounded Knapsack Problem (BKP), where each item type has a set-up weight and a set-up value that are included in the knapsack and the  ...  This paper provides three dynamic programming algorithms that solve BSKP in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS).  ...  Acknowledgments The authors would like to thank the Associate Editor and two anonymous referees for their insightful comments and feedback, which has resulted in a significantly improved manuscript.  ... 
doi:10.1016/j.disopt.2006.11.002 fatcat:zzybpj3orrf5pfzxouf7zusff4

Integer knapsack problems with set-up weights

Laura A. McLay, Sheldon H. Jacobson
2007 Computational optimization and applications  
The Integer Knapsack Problem with Set-up Weights (IKPSW) is a generalization of the classical Integer Knapsack Problem (IKP), where each item type has a set-up weight that is added to the knapsack if any  ...  IKPSW and kIKPSW have applications in the area of aviation security. This paper provides dynamic programming algorithms for each problem that produce optimal solutions in pseudo-polynomial time.  ...  The first author was also supported in part by the program in Arms Control, Disarmament, and International Security (ACDIS) at the University of Illinois.  ... 
doi:10.1007/s10589-007-9020-5 fatcat:2rksbrwqdzaxnnou4k2e75t4mu

A Recursive and Parallelized Dynamic Programming Implementation of Hard Merkle-Hellman Knapsack System for Public Key Cryptography

Vaddadi Sai Rahul, N. Narayanan Prasanth, S. P. Raja
2021 Cybernetics and Information Technologies  
The Hard knapsack variant of Merkle-Hellman is solved first using plain recursion and then improvised using a dynamic programming approach to the problem.  ...  Merkle-Hellman public key cryptosystem is a long-age old algorithm used in cryptography.  ...  Introduction The Knapsack problem is an example of a combinatorial optimization problem, which seeks for a best solution from among many other solutions.  ... 
doi:10.2478/cait-2021-0019 fatcat:lmi6zqxojjcrnlhlqtennoq7ea

Clustering Analysis of Greedy Heuristic Method in Zero_One Knapsack Problem

V. Selvi
2018 International Journal of Emerging Research in Management and Technology  
Knapsack problem is a surely understood class of optimization problems, which tries to expand the profit of items in a knapsack without surpassing its capacity, Knapsack can be solved by several algorithms  ...  In this paper we are introducing greedy heuristic algorithm for solving zero_one knapsack problem.  ...  In many problems, a greedy strategy does not in general produce an optimal solution, but nonetheless a greedy heuristic may yield locally optimal solutions that approximate a global optimal solution in  ... 
doi:10.23956/ijermt.v6i7.181 fatcat:2jxkcins6zfozpg4cumcpbxzsu

Efficient Web Service Composition via Knapsack-Variant Algorithm [article]

Shiliang Fan, Yubin Yang
2018 arXiv   pre-print
Then, each search step on the graph is transformed into a dynamic knapsack problem by mapping services to items whose volume and cost is changeable, after which a knapsack-variant algorithm is applied  ...  In this paper we present an efficient mechanism to solve the problem of web service composition.  ...  dynamic knapsack problem.  ... 
arXiv:1801.09102v1 fatcat:mw4sr7dsxfenldxxki6vcitgim

Genetic Algorithm for a class of Knapsack Problems

Shalin Shah
2019 Zenodo  
The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly.  ...  In this paper, a genetic algorithm is presented for spanner knapsack instances.  ...  The 0/1 Knapsack Problem The 0/1 knapsack problem is defined as follows: given a set of n objects each with weight The problem is a reduction of real world resource allocation problems with constraints  ... 
doi:10.5281/zenodo.3344944 fatcat:dk645j53gbefxpfizyzx6sicyi

An Exact Algorithm for the Unbounded Knapsack Problem with Minimizing Maximum Processing Time

Chanin Srisuwanna, Peerayuth Charnsethi
2007 Journal of Computer Science  
In this study, we proposed a new exact algorithm for this problem, called MMPTUKP algorithm.  ...  We address a variant of the unbounded knapsack problem (UKP) into which the processing time of each item is also put and considered, referred as MMPTUKP.  ...  ACKNOWLEDGEMENT We would like to thank Professor Silvano Martello, University of Bologna, Italy, for many papers and discussions in which contributed significantly for the early version of paper.  ... 
doi:10.3844/jcssp.2007.138.143 fatcat:sgx2prwnjfdwdoi3spzymprpc4

Greedy genetic algorithm to Bounded Knapsack Problem

Sarsij Kaystha, Suneeta Agarwal
2010 2010 3rd International Conference on Computer Science and Information Technology  
This paper proposes an approach to find solution to the Bounded Knapsack Problem (BKP). BKP is a generalization of 0/1 knapsack problem in which multiple  ...  RELATED WORK Many different algorithms to solve the knapsack problem have been evolved. In multiple knapsack problems (MKP), there are a set of containers of various capacity.  ...  Every sub problem is solved by GA to generate a set of suboptimal solutions And in the supervising problem, the elements of each set are optimally combined by GA to yield the optimal solution for the original  ... 
doi:10.1109/iccsit.2010.5563867 fatcat:mofyvpsq25e3bk7am2bgdztoxy

A scalable GPU-based approach to accelerate the multiple-choice knapsack problem

B. Suri, U. D. Bordoloi, P. Eles
2012 2012 Design, Automation & Test in Europe Conference & Exhibition (DATE)  
In this paper, we propose a new GPU-based approach to accelerate the multiple-choice knapsack problem, which is a general version of the 0-1 knapsack problem.  ...  Apart from exploiting the parallelism offered by the GPUs, we also employ a variety of GPU-specific optimizations to further accelerate the running times of the knapsack problem.  ...  In this paper, we focus on the multiplechoice knapsack (MCK) problem because it is a general version of the 0-1 knapsack problem.  ... 
doi:10.1109/date.2012.6176665 dblp:conf/date/SuriBE12 fatcat:3n66fwzqezhprotaenp7mqsdtu

Computational Burden Analysis for Integer Knapsack Problems Solved with Dynamic Programming

Dariusz Horla
2017 Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics  
It presents the efficiency of the algorithms information expressed both in calculation time, as well as mean number of iterations in knapsack problems up to 15,000 items and capacity of the knapsack equal  ...  The paper presents the results concerning computational burden analysis of dynamic programming and bottom-up algorithms when solving knapsack problems.  ...  Mateusz Pacek for his help with formulating the benchmark problem.  ... 
doi:10.5220/0006415302150220 dblp:conf/icinco/Horla17 fatcat:u7a732cvazed3elnwflfutf4ci

Experimental study on population-based incremental learning algorithms for dynamic optimization problems

Shengxiang Yang, Xin Yao
2005 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
In this paper, a new dynamic problem generator that can create required dynamics from any binary-encoded stationary problem is also formalized.  ...  Using this generator, a series of dynamic problems were systematically constructed from several benchmark stationary problems and an experimental study was carried out to compare the performance of several  ...  A New Dynamic Problem Generator In this paper, we formalize a new dynamic problem generator that can generate dynamic test problems from any binary encoded stationary problem.  ... 
doi:10.1007/s00500-004-0422-3 fatcat:ox45pfaqcfhgdc5fuvny337ore

A Dynamic Programming based GA for 0-1 Modified Knapsack Problem

Zaheed Ahmed, Irfan Younas
2011 International Journal of Computer Applications  
In this paper, we design and analyze the Multiple Knapsack Problems (MKP) by using genetic algorithms.  ...  The classical 0-1 knapsack problem is one of the more studied combinatorial optimization problem which belong to the NP class of algorithms.  ...  During its extensive study, a number of extensions and variants have evolved: Multiple knapsack problems (MKP), multidimensional knapsack problems (MDKP), multi choice knapsack problems (MCKP) and multiple  ... 
doi:10.5120/2028-2668 fatcat:elnkqhs3rbacvjnyhw25kgnztm

Exact solution of the robust knapsack problem

Michele Monaci, Ulrich Pferschy, Paolo Serafini
2013 Computers & Operations Research  
We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of  ...  For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities.  ...  While the brief description of the algorithm in [12] relies on a modification of a dynamic program for the nominal knapsack problem, we present a detailed algorithm explicitly designed for (RKP) which  ... 
doi:10.1016/j.cor.2013.05.005 pmid:24187428 pmcid:PMC3727332 fatcat:ynwsoejafrdw5otxng745orflq
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