Nonlinear optimization over a Weighted Independence System

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Date
2008-03-14MFO Scientific Program
Research in Pairs 2007Series
Oberwolfach Preprints;2008,10Author
Lee, Jon
Onn, Shmuel
Weismantel, Robert
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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 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.