Nonlinear Optimization over a Weighted Independence System

Details Nonlinear Optimization over a Weighted Independence System Nonlinear Optimization over a Weighted Independence System

2008-05-07

arxiv.org/abs/0805.0954v1

SIAM Journal on Discrete Mathematics, 23:1667--1681, 2009

Mathematics

Combinatorics

Scientific paper

We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear functions of the total weight of an independent set, where r is a constant that depends on certain Frobenius numbers of the individual weights and is independent of the size of the ground set. In contrast, we show that finding an optimal (0-best) solution requires exponential time even in a very special case of the problem.

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