Shortest Path Routing Algorithms in Multihop Networks

The topic of shortest path algorithms is very fundamental and important in information science and technology. Shortest path algorithms have evolved over many years and have found applications in different domains such as telecommunication networks, military, and transportation. There has been a lot of work undertaken on this topic in this area in the past. A lot of research is still being conducted. The topic is still poorly understood. This article should be helpful to readers, because it reviews some of the important works conducted in the area, out of the plenty of works available on this topic. The problem is so fundamental that whatever the interest areas of the readers may be, they will find the article useful. The popular traditional shortest path algorithms date back to 1958/1959 and were proposed by Dijkstra (1959), and Bellman (1958). Their algorithms found wide applications in the abovementioned domains for many years. However, they were static. Thereafter, many other algorithms were proposed in the last few decades, all of which can be classified to be either dynamic or semi-dynamic.

[1]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[2]  Bruce S. Davie,et al.  Computer Networks: A Systems Approach , 1996 .

[3]  B. John Oommen,et al.  Dynamic algorithms for the shortest path routing problem: learning automata-based solutions , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Peter S Loubai.  A NETWORK EVALUATION PROCEDURE , 1967 .

[5]  Giuseppe F. Italiano,et al.  Incremental algorithms for minimal length paths , 1991, SODA '90.

[6]  Daniele Frigioni,et al.  Fully dynamic output bounded single source shortest path problem , 1996, SODA '96.

[7]  Thomas W. Reps,et al.  On the Computational Complexity of Dynamic Graph Problems , 1996, Theor. Comput. Sci..

[8]  M. Schwartz,et al.  Routing Techniques Used in Computer Communication Networks , 1980, IEEE Trans. Commun..

[9]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[10]  Daniele Frigioni,et al.  Semi-Dynamic Shortest Paths and Breadth-First Search in Digraphs , 1997, STACS.

[11]  Giuseppe F. Italiano,et al.  A new approach to dynamic all pairs shortest paths , 2003, STOC '03.

[12]  Mehdi Khosrow-Pour,et al.  Printed at: , 2011 .

[13]  Giuseppe F. Italiano,et al.  Fully dynamic all pairs shortest paths with real edge weights , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[14]  Philip N. Klein,et al.  Faster Shortest-Path Algorithms for Planar Graphs , 1997, J. Comput. Syst. Sci..

[15]  Daniele Frigioni,et al.  Experimental analysis of dynamic algorithms for the single source shortest paths problem , 1998, JEAL.

[16]  Satish Rao,et al.  Planar graphs, negative weight edges, shortest paths, and near linear time , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[17]  Valerie King,et al.  Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[18]  Daniele Frigioni,et al.  Fully Dynamic Algorithms for Maintaining Shortest Paths Trees , 2000, J. Algorithms.

[19]  Mikko T. Siponen.  On the Role of Human Mortality in Information System Security: From the Problems of Descriptivism to Non-Descriptive Foundations , 2001, Inf. Resour. Manag. J..

[20]  Eric C. Rosen,et al.  The New Routing Algorithm for the ARPANET , 1980, IEEE Trans. Commun..

[21]  Shimon Even,et al.  Updating distances in dynamic graphs , 1985 .

[22]  V. V. Rodionov.  The parametric problem of shortest distances , 1968 .

[23]  Animesh Kr Trivedi,et al.  Mobile Ad Hoc Network Security Vulnerabilities , 2009 .

[24]  Daniele Frigioni,et al.  Maintaining Shortest Paths in Digraphs with Arbitrary Arc Weights: An Experimental Study , 2000, WAE.

[25]  A. Pan,et al.  On Finding and Updating Spanning Trees and Shortest Paths , 1975, SIAM J. Comput..

[26]  Hans Rohnert,et al.  A Dynamization of the All Pairs Least Cost Path Problem , 1985, STACS.