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research article

The VPN problem with concave costs

Fiorini, Samuel
•
Oriolo, Gianpaolo
•
Sanità, Laura  
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2010
Siam Journal of Discrete Mathematics

Only recently Goyal, Olver and Shepherd (Proc. STOC, 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. Alg., 1997) and Gupta, Kleinberg, Kumar, Rastogi and Yener (Proc. STOC, 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 non-decreasing 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.

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Type
research article
DOI
10.1137/090749700
Author(s)
Fiorini, Samuel
Oriolo, Gianpaolo
Sanità, Laura  
Theis, Dirk Oliver
Date Issued

2010

Published in
Siam Journal of Discrete Mathematics
Volume

24

Issue

3

Start page

1080

End page

1090

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
DISOPT  
Available on Infoscience
February 3, 2010
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/46415
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