Inverse 1-median Problem on Trees under Weighted l ∞ Norm
The inverse 1-median problem is concerned with modifying the weights of the customers at minimum cost such that a prespecified supplier becomes the 1-median of modified location problem. We first present the model of inverse 1-median problem on trees. Then we propose two algorithms to solve the problem under weighted l ∞ norm with bound constraints on modifications. Based on the approach of the unbounded case, we devise a greedy-type algorithm which runs in O(n 2) time, where n is the number of vertices. Based on the property of the optimal solution, we propose an O(n logn) time algorithm using the binary search.
KeywordsInverse 1-median problem Tree weighted l ∞ norm Binary search
Unable to display preview. Download preview PDF.
- 1.Alizadeh, B., Burkard, R.E.: Combinatorial algorithms for inverse absolute and vertex 1-center location problems on trees. Technical Report, Graz University of Technology (2009), http://www.math.tugraz.at/fosp/pdfs/tugraz_0143.pdf
- 4.Bonab, F.B., Burkard, R.E., Alizadeh, B.: Inverse Median Location Problems with Variable Coordinates. Central European Journal of Operations Research (2009), doi:10.1007/s10100-009-0114-2Google Scholar
- 5.Burkard, R.E., Galavii, M., Gassner, E.: The inverse Fermat-Weber problem. Technical Report, Graz University of Technology (2008), http://www.math.tugraz.at/fosp/pdfs/tugraz_0107.pdf
- 9.Galavii, M.: Inverse 1-Median Problems, Ph.D. Thesis, Institute of Optimization and Discrete Mathematics, Graz University of Technology, Graz, Austria (2008)Google Scholar
- 12.Goldman, A.J.: Optimal center location in simple networks. Transportation Science 2, 77–91 (1962)Google Scholar
- 13.Hua, et al.: Applications of mathematical models to wheat harvesting. Acta Mathematica Sinica 11, 63–75 (1961) (in Chinese); English Translation in Chinese Math. 2, 77–91 (1962)Google Scholar