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.
This research was supported in part by the Mathematisches Forschungsinstitut Oberwolfach through the Research in Pairs Programme.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstein, Y., Lee, J., Maruri-Aguilar, H., Onn, S., Riccomagno, E., Weismantel, R., Wynn, H.: Nonlinear matroid optimization and experimental design. SIAM Journal on Discrete Mathematics 22, 901–919 (2008)
Berstein, Y., Onn, S.: Nonlinear bipartite matching. Discrete Optimization 5, 53–65 (2008)
Brauer, A.: On a problem of partitions. American Journal of Mathematics 64, 299–312 (1942)
Lee, J., Onn, S., Weismantel, R.: Nonlinear optimization over a weighted independence system. Oberwolfach Preprint Series OWP 2008 – 10, http://www.mfo.de/publications/owp/2008/OWP2008_10.pdf
Mulmuley, K., Vazirani, U.V., Vazirani, V.V.: Matching is as easy as matrix inversion. Combinatorica 7, 105–113 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lee, J., Onn, S., Weismantel, R. (2009). Nonlinear Optimization over a Weighted Independence System. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-02158-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02157-2
Online ISBN: 978-3-642-02158-9
eBook Packages: Computer ScienceComputer Science (R0)