Nonlinear Optimization over a Weighted Independence System

Authors:
Jon Lee;Shmuel Onn;Robert Weismantel
Affiliations:
IBM T.J. Watson Research Center, Yorktown Heights, USA NY 10598;Technion - Israel Institute of Technology, Haifa, Israel 32000;Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany D-39106
Venue:
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Year:
2009

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Abstract

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 depending on certain Frobenius numbers of the 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.