Notions of Connectivity in Overlay Networks
“How well connected is the network?” This is one of the most fundamental questions one would ask when facing the challenge of designing a communication network. Three major notions of connectivity have been considered in the literature, but in the context of traditional (single-layer) networks, they turn out to be equivalent. This paper introduces a model for studying the three notions of connectivity in multi-layer networks. Using this model, it is easy to demonstrate that in multi-layer networks the three notions may differ dramatically. Unfortunately, in contrast to the single-layer case, where the values of the three connectivity notions can be computed efficiently, it has been recently shown in the context of WDM networks (results that can be easily translated to our model) that the values of two of these notions of connectivity are hard to compute or even approximate in multi-layer networks. The current paper shed some positive light into the multi-layer connectivity topic: we show that the value of the third connectivity notion can be computed in polynomial time and develop an approximation for the construction of well connected overlay networks.
KeywordsOverlay networks graph theory connectivity approximation
Unable to display preview. Download preview PDF.
- 2.Cisco IOS Software Releases 12.0 S. Mpls traffic engineering: Shared risk link groups (srlg), http://www.cisco.com/en/US/docs/ios/12_0s/feature/guide/fs29srlg.html
- 3.Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)Google Scholar
- 5.Dinic, E.A.: Algorithm for Solution of a Problem of Maximum Flow in a Network with Power Estimation. Soviet Math Doklady 11, 1277–1280 (1970)Google Scholar
- 9.Grotschel, M., Lovasz, L., Schrijver, A.: Geometric algorithms and combinatorial optimization. Combinatorica (1981)Google Scholar
- 10.Hastad, J.: Clique is hard to approximate within n 1 − ε. In: IEEE Annual Symposium on Foundations of Computer Science, p. 627 (1996)Google Scholar
- 11.Kleinberg, J., Tardos, E.: Algorithm Design. Addison Wesley (2006)Google Scholar
- 13.Menger, K.: Zur allgemeinen kurventheorie. Fund. Math. 10(95-115), 5 (1927)Google Scholar
- 14.Network Protection Website. Network protection techniques, network failure recovery, network failure events, http://www.network-protection.net/shared-risk-link-group-srlg/
- 15.Ramamurthy, S., Mukherjee, B.: Survivable wdm mesh networks. part i-protection. In: Proceedings of IEEE Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 1999, vol. 2, pp. 744–751 (March 1999)Google Scholar
- 16.White Paper, Cisco Systems Inc. Policy-based routing (1996), http://www.cisco.com/warp/public/cc/pd/iosw/tech/plicy_wp.pdf