On k-sum optimization

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 ε-approximation scheme then KSOP can also be solved by a polynomial time ε-approximation scheme.