An entropy maximization problem in shortest path routing networks

In the context of an IP network, we investigate an interesting case of the inverse shortest path problem using the concept of network centrality. For a given network, the centrality distribution associated with the links of a network can be determined based on the number of shortest paths passing through each link. An entropy measure for this distribution is defined, and we then forumulate the inverse shortest problem in terms of maximizing this entropy. We then obtain a centrality distribution that is as broadly distributed as possible subject to the topology constraints. An appropriate change in the weight of a link alters the number of shortest paths that pass through it, thereby modifying the centrality distribution. The idea is to obtain a centrality distribution that maximizes the entropy. This problem is shown to be NP-hard, and a heuristic approach is proposed. An application to handling link failure scenarios in Open Shortest Path First routing is discussed.

[1]  R. S. Singh,et al.  Traffic planning in a constrained network using entropy maximisation approach , 2005 .

[2]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[3]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[4]  Matthias Dehmer,et al.  Entropy and the Complexity of Graphs Revisited , 2012, Entropy.

[5]  S. Borgatti,et al.  Betweenness centrality measures for directed graphs , 1994 .

[6]  Cheng-Huang Hung.  On the inverse shortest path length problem , 2003 .

[7]  Krishna M. Sivalingam,et al.  Application of entropy of centrality measures to routing in tactical wireless networks , 2013, 2013 19th IEEE Workshop on Local & Metropolitan Area Networks (LANMAN).

[8]  Mung Chiang,et al.  Link-State Routing With Hop-by-Hop Forwarding Can Achieve Optimal Traffic Engineering , 2011, IEEE/ACM Trans. Netw..

[9]  Anna Nagurney,et al.  On a Paradox of Traffic Planning , 2005, Transp. Sci..

[10]  M. Piórob,et al.  On OSPF Related Network Optimisation Problems , 2022 .

[11]  Sadiq M. Sait,et al.  OSPF Weight Setting Optimization for Single Link Failures , 2011, ArXiv.

[12]  Mikkel Thorup,et al.  Increasing Internet Capacity Using Local Search , 2004, Comput. Optim. Appl..

[13]  Daniel Massey,et al.  Destination reachability and BGP convergence time [border gateway routing protocol] , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[14]  Mikael Call,et al.  Inverse Shortest Path Routing Problems in the Design of IP Networks , 2010 .

[15]  K. G. Ramakrishnan,et al.  Optimal routing in shortest-path data networks , 2001, Bell Labs Technical Journal.

[16]  Didier Burton,et al.  On the Inverse Shortest Path Problem , 1993 .

[17]  J. N. Kapur.  Maximum-entropy models in science and engineering , 1992 .

[18]  Yuval Shavitt,et al.  Beyond centrality—classifying topological significance using backup efficiency and alternative paths , 2007, Networking.

[19]  Michal Pióro,et al.  On open shortest path first related network optimisation problems , 2002, Perform. Evaluation.

[20]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[21]  J. A. TOMLIN,et al.  Traffic Distribution and Entropy , 1968, Nature.

[22]  Srihari Nelakuditi,et al.  On Selection of Paths for Multipath Routing , 2001, IWQoS.