CFP last date
16 December 2024
Reseach Article

An Efficient Technique for Computing Shortest Path Tree in Dynamic Graphs

by Neeraj Kumar Maurya, R. R. Sedamkar
International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
Volume 7 - Number 1
Year of Publication: 2014
Authors: Neeraj Kumar Maurya, R. R. Sedamkar
10.5120/ijais14-451133

Neeraj Kumar Maurya, R. R. Sedamkar . An Efficient Technique for Computing Shortest Path Tree in Dynamic Graphs. International Journal of Applied Information Systems. 7, 1 ( April 2014), 42-48. DOI=10.5120/ijais14-451133

@article{ 10.5120/ijais14-451133,
author = { Neeraj Kumar Maurya, R. R. Sedamkar },
title = { An Efficient Technique for Computing Shortest Path Tree in Dynamic Graphs },
journal = { International Journal of Applied Information Systems },
issue_date = { April 2014 },
volume = { 7 },
number = { 1 },
month = { April },
year = { 2014 },
issn = { 2249-0868 },
pages = { 42-48 },
numpages = {9},
url = { https://www.ijais.org/archives/volume7/number1/615-1133/ },
doi = { 10.5120/ijais14-451133 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2023-07-05T18:54:32.401317+05:30
%A Neeraj Kumar Maurya
%A R. R. Sedamkar
%T An Efficient Technique for Computing Shortest Path Tree in Dynamic Graphs
%J International Journal of Applied Information Systems
%@ 2249-0868
%V 7
%N 1
%P 42-48
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper proposes an efficient technique for computing shortest path in dynamic graph. Which finds shortest path in a given graph which is static or intended to change its weight frequently. If that graph is static i. e. not changing its weight then SPT is being calculated once and that remains same. If graph is dynamic i. e. changing its weight then this technique finds new SPT with traversing minimum number of nodes or vertices. This technique extends a few state-of-the-art dynamic SPT algorithms to handle multiple edge weight updates, and find the SPT. A function based on the location of current node/ state is used to vary the cost of the goal node and the search is done with minimum the state space and exploring only affected nodes, by using these approaches problem is solved in minimum time. Based on experimental results on sample data set we propose to device an algorithm which efficiently handles different traffic conditions. The performance of this algorithm is measured on the basis of Graph size, number of changed edge (NCE). To evaluate the proposed dynamic algorithm, comparison is done with the well-known static Dijkstra algorithm. Where proposed algorithm's complexity is O(bd) in worst case O(E) in average case and O(1) in best case.

References
  1. D. Frigioni, A. Marchetti-Spaccamela, and U. Nanni, "Fully Dynamic Algorithms for Maintaining Shortest Paths Trees," J. Algorithms, vol. 34, no. 2, pp. 251-281, 2000.
  2. D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasquale, "Experimental Analysis of Dynamic Algorithms for the Single-Source Shortest- Path Problem," ACM J. Experimental Algorithms, vol. 3, p. 5, 1998.
  3. P. Narva´ez, K. Siu, and H. Tzeng, "New Dynamic Algorithms for Shortest Path Tree Computation," ACM Trans. Networking, vol. 8, no. 6, pp. 734-746, 2000.
  4. P. Narva´ez, K. Siu, and H. Tzeng, "New Dynamic SPT Algorithm Based on a Ball-and-String Model," ACM Trans. Networking, vol. 9, no. 6, pp. 706-718, 2001.
  5. Edward P. F. Chan and Yaya Yang,"Shortest Path Tree Computation in Dynamic Graph,"IEEE Transaction On Computers, vol 58. No. 4. , April 2009.
  6. G. Ramalingam and T. W. Reps, "An Incremental Algorithm for a Generalization of the Shortest-Path Problem," J. Algorithms, vol. 21, no. 2, pp. 267-305, 1996. [7 ] E. W. Dijkstra, "A Note on Two Problems in Connection with Graphs," Numerical Math. , vol. 1, pp. 269-271, 1959.
  7. B. Xiao, Q. Zhuge, and E. H. -M. Sha, "Efficient Algorithms forDynamic Update of Shortest Path Tree in Networking," J. Computers and Their Applications, vol. 11, no. 1, 2003.
  8. G. Ramalingam and T. W. Reps, "On the Computational Complexity of Dynamic Graph Problems," Theoretical Computer Science, vol. 158, nos. 1-2, pp. 233-277, 1996.
  9. G. Ausiello, G. F. Italiano, A. Marchetti-Spaccamela, and U. Nanni,"Incremental Algorithms for Minimal Length Paths," J. Algorithms,vol. 12, no. 4, pp. 615-638, 1991.
Index Terms

Computer Science
Information Sciences

Keywords

Dynamic Dijkstra Dynamic Graph Graph Directed Graph.