k-Sum optimization problems

Authors:
S. K. Gupta;A. P. Punnen
Affiliations:
Mathematics Department, Indian Institute of Technology, Kanpur 208 016, India;Mathematics Department, Indian Institute of Technology, Kanpur 208 016, India
Venue:
Operations Research Letters
Year:
1990

Citing 4
Cited 1

Efficient algorithms for finding minimum spanning trees in undirected and directed graphs

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Combinatorial optimization: algorithms and complexity

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Balanced optimization problems

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Minimum deviation problems

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On k-sum optimization

Operations Research Letters

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Abstract

We consider a family of subsets of a finite set, each of cardinality n, as feasible solutions of a combinatorial optimization problem. Using weights associated with the elements of the given finite set, k-sum optimization problems and k-sum deviation problems are defined. We show that such problems can be solved efficiently if the n-sum problem can be solved efficiently. If the family F is the base system of a matroid, the k-sum optimization problem can be solved by a greedy algorithm. The solutions of k-sum optimization problems are used to give a new characterization of matroids. The k-sum spanning tree problem is also considered. Using an algorithm to obtain minmax spanning trees, a decomposition algorithm is proposed to solve such problems. This decomposition algorithm can also be used to improve the efficiency of most of the known minimum spanning tree algorithms.