Stochastic learning automata-based dynamic algorithms for the single source shortest path problem

This paper presents the first Learning Automaton solution to the Dynamic Single Source Shortest Path Problem. It involves finding the shortest path in a singlesource stochastic graph, where there are continuous probabilistically- based updates in edge-weights. The algorithm is a few orders of magnitude superior to the existing algorithms. It can be used to find the shortest path within the "statistical" average graph, which converges irrespective of whether there are new changes in edge-weights or not. On the other hand, the existing algorithms will fail to exhibit such a behavior and would recalculate the affected shortest paths after each weight change. The algorithm can be extremely useful in application domains including transportation, strategic planning, spatial database systems and networking.

[1]  B. John Oommen,et al.  Graph Partitioning Using Learning Automata , 1996, IEEE Trans. Computers.

[2]  Mohammad S. Obaidat,et al.  Guest editorial learning automata: theory, paradigms, and applications , 2002, IEEE Trans. Syst. Man Cybern. Part B.

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

[4]  Ann Nowé,et al.  Colonies of learning automata , 2002, IEEE Trans. Syst. Man Cybern. Part B.

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

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

[7]  S. Lakshmivarahan,et al.  Learning Algorithms Theory and Applications , 1981 .

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

[9]  B. John Oommen,et al.  Continuous Learning Automata Solutions to the Capacity Assignment Problem , 2000, IEEE Trans. Computers.

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

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

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

[13]  Kai-Yeung Siu,et al.  New dynamic algorithms for shortest path tree computation , 2000, TNET.

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