On k-sum optimization

Authors:
Abraham P. Punnen;Y. P. Aneja
Affiliations:
Department of Mathematics, Statistics and Computer Science, University of New Brunswick, Saint John, N.B., Canada;Faculty of Business Administration, University of Windsor, Windsor, Ontario, Canada N9B 3P4
Venue:
Operations Research Letters
Year:
1996

Citing 2
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Abstract

The k-sum optimization problem (KSOP) is the combinatorial problem of finding a solution such that the sum of the weights of the k largest weighted elements of the solution is as small as possible. KSOP simultaneously generalizes both bottleneck and minsum problems. We show that KSOP can be solved in polynomial time whenever an associated minsum problem can be solved in polynomial time. Further we show that if the minsum problem is solvable by a polynomial time @e-approximation scheme then KSOP can also be solved by a polynomial time @e-approximation scheme.