par Fiorini, Samuel 
;Oriolo, Gianpaolo;Sanità, Laura;Theis, Dirk
Référence SIAM journal on discrete mathematics, 24, 3, page (1080-1090)
Publication Publié, 2010
;Oriolo, Gianpaolo;Sanità, Laura;Theis, Dirk Référence SIAM journal on discrete mathematics, 24, 3, page (1080-1090)
Publication Publié, 2010
Article révisé par les pairs
| Résumé : | Only recently Goyal, Olver, and Shepherd [Pr oc. STOC, ACM, New York, 2008] proved that the symmetric virtual private network design (sVPN) problem has the tree routing property, namely, that there always exists an optimal solution to the problem whose support is a tree. Combining this with previous results by Fingerhut, Suri, and Turner [J. Algorithms, 24 (1997), pp. 287-309] and Gupta et al. [Proc. STOC, ACM, New York, 2001], sVPN can be solved in polynomial time. In this paper we investigate an APX-hard generalization of sVPN, where the contribution of each edge to the total cost is proportional to some non-negative, concave, and nondecreasing function of the capacity reservation. We show that the tree routing property extends to the new problem and give a constant-factor approximation algorithm for it. We also show that the undirected uncapacitated single-source minimum concave-cost flow problem has the tree routing property when the cost function has some property of symmetry. © 2010 Societ y for Industrial and Applied Mathematics. |
