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Article information
2015 , Volume 20, ¹ 6, p.72-86
Prolubnikov A.V.
The set cover problem with interval weights and the greedy algorithm for its solution
Purpose: We study the set cover problem when a set of weighted subsets of a set U is supposed to be given. Cover set of U is a collection of subsets of that set when the union of members of the set contains U. We need to choose a cover that contains sets which have minimum total weight. The specificity of our work is that we investigate the problem with interval weights of the subsets. Methodology: We introduce definitions of optimal and approximate solutions of the problem. Realization of the weights of given subsets is a possible variant of these weights. The weak optimal solution of the problem is a solution that is optimal for some realization. The strong optimal solution is a solution that is optimal for any realization. The united optimal solution is such a set of weak solutions that it contains an optimal solution for any possible realization. The united approximate solution is such a set of covers that contains approximate solutions for every realization. Findings: The theorem of characterization of the strong optimal solution is proved. The modification of the greedy algorithm for the problem is presented. The algorithm gives the united approximate solution as a result. For the uniform distributions of weights, we present a modification of the algorithm that could be used to find probabilities of the approximate solutions. Originality/value: The concepts of optimal and approximate solutions are presented for the set cover problem with interval weights. The theorem of characterization of the strong optimal solution is proved. The modification of the greedy algorithm for the set cover problem with interval weights is presented.
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Keywords: set cover problem, interval uncertainty, greedy algorithm
Author(s):
Prolubnikov Alexander Vyacheslavovich
Associate Professor
Office: Omsk F.M. Dostoevsky State University
Address: 644077, Russia, Omsk, Mira avenue 55-a
Phone Office: (3812) 64-42-38
E-mail: a.v.prolubnikov@mail.ru
SPIN-code: 4729-9643 References:
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Bibliography link:
Prolubnikov A.V. The set cover problem with interval weights and the greedy algorithm for its solution // Computational technologies. 2015. V. 20. ¹ 6. P. 72-86
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