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Virtual Private Network Design: A Proof of the Tree Routing Conjecture on Ring Networks

Authors:

C. A. J. Hurkens,

J. C. M. Keijsper,

L. StougieAuthors Info & Claims

SIAM Journal on Discrete Mathematics, Volume 21, Issue 2

Pages 482 - 503

https://doi.org/10.1137/050626259

Published: 01 April 2007 Publication History

Abstract

A basic question in virtual private network (VPN) design is if the symmetric version of the problem always has an optimal solution which is a tree network. An affirmative answer would imply that the symmetric VPN problem is solvable in polynomial time. We give an affirmative answer in case the communication network, within which the VPN must be created, is a circuit. This seems to be an important step towards answering the general question. The proof relies on a dual pair of linear programs and actually implies an even stronger property of VPNs. We show that this property also holds for some other special cases of the problem, in particular when the network is a tree of rings.

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Saenko IKotenko I(2018)Genetic Algorithms for Solving Problems of Access Control Design and Reconfiguration in Computer NetworksACM Transactions on Internet Technology10.1145/309389818:3(1-21)Online publication date: 6-Mar-2018
https://dl.acm.org/doi/10.1145/3093898
Fréchette AShepherd FThottan MWinzer P(2015)Shortest path versus multihub routing in networks with uncertain demandIEEE/ACM Transactions on Networking10.1109/TNET.2014.235357623:6(1931-1943)Online publication date: 1-Dec-2015
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Pinto-Roa DBrizuela CBarán B(2015)Multi-objective routing and wavelength converter allocation under uncertain trafficOptical Switching and Networking10.1016/j.osn.2014.10.00116:C(1-20)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1016/j.osn.2014.10.001
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Virtual Private Network Design: A Proof of the Tree Routing Conjecture on Ring Networks

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cover image SIAM Journal on Discrete Mathematics

SIAM Journal on Discrete Mathematics Volume 21, Issue 2

April 2007

278 pages

ISSN:0895-4801

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 April 2007

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Saenko IKotenko I(2018)Genetic Algorithms for Solving Problems of Access Control Design and Reconfiguration in Computer NetworksACM Transactions on Internet Technology10.1145/309389818:3(1-21)Online publication date: 6-Mar-2018
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Fréchette AShepherd FThottan MWinzer P(2015)Shortest path versus multihub routing in networks with uncertain demandIEEE/ACM Transactions on Networking10.1109/TNET.2014.235357623:6(1931-1943)Online publication date: 1-Dec-2015
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Olver NShepherd F(2014)Approximability of Robust Network DesignMathematics of Operations Research10.1287/moor.2013.062039:2(561-572)Online publication date: 1-May-2014
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Moradi ALodi AHashemi S(2014)On the difficulty of virtual private network instancesNetworks10.1002/net.2154863:4(327-333)Online publication date: 1-Jul-2014
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Goyal NOlver NShepherd F(2013)The VPN Conjecture Is TrueJournal of the ACM10.1145/2487241.248724360:3(1-17)Online publication date: 1-Jun-2013
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Grandoni FRothvoß T(2010)Network design via core detouring for problems without a coreProceedings of the 37th international colloquium conference on Automata, languages and programming10.5555/1880918.1880972(490-502)Online publication date: 6-Jul-2010
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A short proof of the VPN Tree Routing Conjecture on ring networks

Towards a proof of the 2-to-1 games conjecture?

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