An Efficient Algorithm for the 0-1 Knapsack Problem

Nauss, Robert M.

doi:10.1287/mnsc.23.1.27

Cited by 118 publications

(32 citation statements)

References 7 publications

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“…In the middle of the 1970s -several good algorithms for Knapsack Problem (KP) were developed [16], [17], [18]. The starting point of each of these algorithms was to order the variables according to non-increasing profitto-weight (pj/wj) ratio, which was the basis for solving the Linear KP.‖ Given a knapsack of limit, Z, and n dissimilar items, Caceres and Nishibe [7] algorithm resolved the single Knapsack problem using local computation time with communication rounds.…”

Section: Related Workmentioning

confidence: 99%

Optimizing Memory using Knapsack Algorithm

Asamoah¹,

Baidoo²,

Oppong³

2017

IJMECS

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Abstract-Knapsack problem model is a general resource distribution model in which a solitary resource is allocated to various choices with the aim of amplifying the aggregate return. Knapsack problem has been broadly concentrated on in software engineering for a considerable length of time. There exist a few variations of the problem. The study was about how to select contending data/processes to be stacked to memory to enhance maximization of memory utilization and efficiency. The occurrence is demonstrated as 0 -1 single knapsack problem. In this paper a Dynamic Programming (DP) algorithm is proposed for the 0/1 one dimensional knapsack problem. Problem-specific knowledge is integrated in the algorithm description and assessment of parameters, with a specific end goal to investigate the execution of finite-time implementation of Dynamic Programming.

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Section: Related Workmentioning

confidence: 99%

Optimizing Memory using Knapsack Algorithm

Asamoah¹,

Baidoo²,

Oppong³

2017

IJMECS

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“…The algorithm used the best bound selection rule and branching was done on the fractional variable. The large computer memory requirements of this algorithm led to the development of other Branch-and-Bound algorithms by Horowitz and Sahni [7], Nauss [14], Fayard and Plateau [6] and Martello and Toth [11], to name but a few.…”

Section: Historical Notes On Exact Algorithmsmentioning

confidence: 99%

A partitioning scheme for solving the 0-1 knapsack problem

Kruger¹,

Hattingh²

2014

ORiON

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The application of valid inequalities to provide relaxations which can produce tight bounds, is now common practice in Combinatorial Optimisation. This paper attempts to complement current theoretical investigations in this regard. We experimentally search for "valid" equalities which have the potential of strengthening the problem's formulation.Recently, Martello and Toth [13] included cardinality constraints to derive tight upper bounds for the 0-1 Knapsack Problem. Encouraged by their results, we partition the search space by using equality cardinality constraints. Instead of solving the original problem, an equivalent problem, which consists of one or more 0-1 Knapsack Problem with an exact cardinality bound, is solved.By explicitly including a bound on the cardinality, one is able to reduce the size of each subproblem and compute tight upper bounds. Good feasible solutions found along the way are employed to reduce the computational effort by reducing the number of trees searched and the size of the subsequent search trees.We give a brief description of two Lagrangian-based Branch-and-Bound algorithms proposed in Kruger [9] for solving the exact cardinality bounded subproblems and report on results of numerical experiments with a sequential implementation. Implications for and strategies towards parallel implementation are also given.

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“…Given a pile of item [16], each with different weights is it possible to put some of them in a bag (i.e. knapsack) in such a way that the knapsack has a certain weight.…”

Section: The Knapsack Problemmentioning

confidence: 99%

Comparison among different Cryptographic Algorithms using Neighborhood-Generated Keys

Singh¹,

Bharti²

2013

IJCA

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The prevention of information from unauthorized access is the main concern in the area of cryptography. There are various algorithms i.e. Elgamal, RSA, diffie Hellman, Knapsack are proposed with varying key length and key management methods. The size of encrypted message, key management method and algorithm efficiency is critical in respect of implementation in organizations that store large volumes of data. This paper proposes the comparison among various algorithms for different cryptography algorithms used in generating the neighborhood keys.

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An Efficient Algorithm for the 0-1 Knapsack Problem

Cited by 118 publications

References 7 publications

Optimizing Memory using Knapsack Algorithm

Optimizing Memory using Knapsack Algorithm

A partitioning scheme for solving the 0-1 knapsack problem

Comparison among different Cryptographic Algorithms using Neighborhood-Generated Keys

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