CN  Vol.4 No.1 , February 2012
Usage of Pythagorean Triple Sequence in OSPF
Abstract: Shutting down a link for the purposes of a scheduled routine maintenance does cause the forwarding path to change. If these changes are not done in a required order will cause not only transient micro loops but also an overload in some links. Currently, some ISP operators use a graceful link shutdown procedure by first setting up the Interior Gateway Protocol (IGP) link metric to MAX_METRIC -1 and then shutdown the link. In this paper, we present a Pythagorean Triple Metric Sequence as a method to use to shutdown a link during such network operations. Conducting a link shutdown of any desired link for maintenance purpose is a very delicate duty that requires extreme care to prevent transient loops during such topological changes. We thus wish to demonstrate that there exists a Pythagorean Triple Metric Sequence for any given link that can be used to shutdown a link during the routine maintenance by ISPs.
Cite this paper: S. Tembo, K. Yukimatsu, S. Kamamura, T. Miyamura, K. Shiomoto and A. Hiramatsu, "Usage of Pythagorean Triple Sequence in OSPF," Communications and Network, Vol. 4 No. 1, 2012, pp. 73-82. doi: 10.4236/cn.2012.41010.

[1]   P. Francois, M. Shand and O. Bonaventure, “Disruption Free Topology Reconfiguration in OSPF Networks,” Proceedings of IEEE INFOCOM, Anchorage, 6-12 May 2007.

[2]   A. Markopoulou, G. Iannaccone, S. Bhattacharyya, C.-N.Chuah and C. Doit, “Characterization of Failures in an IP Backbone,” IEEE INFOCOM, Vol. 4, 2004, pp. 2307-2317.

[3]   R. Teixeria and J. Rexford, “Managing Routing Disruptions in Internet Service Provider Networks,” IEEE Communications Magazine, Vol. 44, No. 3, 2006, pp. 160-165. doi:10.1109/MCOM.2006.1607880

[4]   L. Shi, J. Fu and X. Fu, “Loop-Free Forwarding Table Updates with Minimal Link Overflow,” Proceeding of IEEE ICC, Dresden, 14-18 June 2009, pp. 1-6.

[5]   C. C. Chen and T. A. Peng, “Almost-Isosceles Right-Angled Triangles,” Australian Journal of Combinatory, Vol. 11, 1995, pp. 263-267.

[6]   J. Kocik, “Clifford Algebras and Euclid’s Parameterization of Pythagorean Triples,” Advances in Applied Clifford Algebras, Vol. 17, 2007, pp. 71-93.

[7]   J. Fu, P. Sj?din and G. Karlsson, “Loop-Free Updates of Forwarding Tables,” IEEE Transactions on Network and Service Management, Vol. 5, No. 1, 2008, pp. 22-35. doi:10.1109/TNSM.2008.080103

[8]   S. S. W. Lee, P. K. Tseng and A. Chen, “Link Weight Assignment and Loop-Free Routing Table Update for Link State Routing Protocols in Energy-Aware Internet,” Future Generation Computer Systems, Vol. 28, No. 2, 2011, pp. 437-439. doi:10.1016/j.future.2011.05.003

[9]   R. Albert and A.-L. Barabasi, “Statistical Mechanics of Complex Networks,” Review of Modern Physics, Vol. 74, No. 1, 2002, pp. 47-97. doi:10.1103/RevModPhys.74.47

[10]   M. E. J. Newman, “The Structure and Function of Complex Networks,” SIAM Society for Industrial and Applied Mathematics, Vol. 45, No. 2, 2003, pp. 167-256.

[11]   X. F. Wang and G. Chen “Complex Networks-Small-World, Scale-Free and Beyond,” IEEE Circuits and Systems Magazine, Vol. 3, No. 1, 2003, pp. 6-20. doi:10.1109/MCAS.2003.1228503