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Inverse Shortest Path in a Graph with Rough Edge Weights

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 148 - Number 6
Year of Publication: 2016
Authors:
Sagarika Biswal, S. P. Mohanty
10.5120/ijca2016911143

Sagarika Biswal and S P Mohanty. Inverse Shortest Path in a Graph with Rough Edge Weights. International Journal of Computer Applications 148(6):6-11, August 2016. BibTeX

@article{10.5120/ijca2016911143,
	author = {Sagarika Biswal and S. P. Mohanty},
	title = {Inverse Shortest Path in a Graph with Rough Edge Weights},
	journal = {International Journal of Computer Applications},
	issue_date = {August 2016},
	volume = {148},
	number = {6},
	month = {Aug},
	year = {2016},
	issn = {0975-8887},
	pages = {6-11},
	numpages = {6},
	url = {http://www.ijcaonline.org/archives/volume148/number6/25759-2016911143},
	doi = {10.5120/ijca2016911143},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

The inverse shortest path problem occurs mostly in reconstruction type of problems where, minimum modifications of the edge weights of a network are made to make a predetermined path to be shortest. In this paper, initially the edge weights are taken as rough variables which, are based on the subjective estimation of the experts. Then these rough weights are approximated by normal uncertain variables and an uncertain programming model has been developed. Further, the uncertain programming model is transformed into a deterministic counterpart which can be solved by any standard method.

References

  1. Burton, D., and Toint, P. L., 1992. On an instance of the inverse shortest path problem. Mathematical programming, 53(1-3), 45-61.
  2. Xu, S. J., and Zhang, J. Z., 1995. An inverse problem of the weighted shortest path problem. Japan J. of industrial and Applied Mathematics, 12(1), 47-59.
  3. Zhang, J. Z., and Liu, Z. H., 1999. A further study on inverse linear programming problems, J. Computational and Applied Mathematics, 106(2), 345-359.
  4. Hu, Z. Q., and Liu, Z. H., 1998. A strongly polynomial algorithm for the inverse shortest arborescence problem, Discrete Applied Mathematics, 82(1-3), 135-154.
  5. Liu, B., 2007. Uncertainty theory, Springer-Verlag, Berlin.
  6. Zhou, J., Yang, F., and Wang, K.., 2014. An inverse shortest path problem on an uncertain graph, Journal of Networks, 9(9), 2353-2359.
  7. Liu, B., 2004. Uncertainty Theory: An introduction to its axiomatic foundation, Springer-Verlag, Berlin.
  8. Zhang, J. Z., Ma, Z. F., and Yang, C., 1995. A column generation method for inverse shortest path problem, Mathematical Methods of Operations Research, 41(3), 347-358.
  9. Liu, B., 2010. A branch of mathematics for modelling human uncertainty, Springer-Verlag, Berlin
  10. Liu, B., 2009. Some research problems in uncertainty theory, Journal of Uncertain Systems, 3(1), 3-10

Keywords

Shortest path, Inverse shortest path, Uncertain variable, Rough variable, Linear programming problem.