ON K-SUM OPTIMIZATION

The k-sum optimization problem (KSOP) is the combinatorial problem of finding a solution such that the sum of the weights or the ii largest weighted elements of the solution is as small as possible. KSOP simult aneously generalizes both bottleneck and minsum problems. We show that KSOP can be solved in polynomial time whenever an associated minsum p roblem can be solved in polynomial time. Further we show that if the m insum problem is solvable by a polynomial time epsilon-approximation s cheme then KSOP can also be solved by a polynomial time epsilon-approx imation scheme.