Skip to main content
SpringerLink
Log in

Faster algorithm to find anti-risk path between two nodes of an undirected graph

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

For a weighted 2-edge connected graph G=(V,E), we are to find a “minimum risk path” from source s to destination t. This is a shortest s−t path under the assumption that at most one edge on the path may be blocked. The fact that the edge is blocked is known only when we reach a site adjacent to the blocked edge.

If n and m are the number of nodes and edges of G, then we show that this problem can be solved in O(n 2) time using only simple data structures. This is an improvement over the previous O(mn+n 2logn) time algorithm. Moreover, with use of more complicated data structures like Fibonacci Heaps and transmuters the time can be further reduced to O(m+nlogn).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1
Fig. 2

Similar content being viewed by others

References

  • Aho AV, Hopcroft JE, Ullman JD (1974) The design and analysis of computer algorithms. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Deo N (1974) Graph theory with applications to engineering and computer science. Prentice-Hall, New York

    MATH  Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(4):269–271

    Article  MATH  MathSciNet  Google Scholar 

  • Fredman M, Tarjan R (1987) Fibonacci heaps and their uses in improved network optimization algorithms. J ACM 34(3):596–615

    Article  MathSciNet  Google Scholar 

  • Nardelli E, Proietti G, Widmayer P (2001) Faster computation of the most vital edge of a shortest path. Inf Process Lett 79:81–85

    Article  MATH  MathSciNet  Google Scholar 

  • Nardelli E, Proietti G, Widmayer P (1998) Finding the detour-critical edge of a shortest path between two nodes. Inf Process Lett 67(1):51–54

    Article  MathSciNet  Google Scholar 

  • Yuan H, Attalah M (2010) Data structures for range minimum queries in multidimensional arrays. In: SODA’10, pp 150–160

    Google Scholar 

  • Tarjan R (1979) Applications of path compression on balanced trees. J ACM 26:690–715

    Article  MATH  MathSciNet  Google Scholar 

  • Tarjan R (1982) Sensitivity analysis of minimum spanning trees and shortest path trees. Inf Process Lett 14(1):30–33

    Article  MathSciNet  Google Scholar 

  • Xiao P, Xu Y, Su B (2009) Finding an anti-risk path between two nodes in undirected graphs. J Comb Optim 17:235–246

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank an anonymous referee for a very careful reading of the manuscript, and his/her critical comments and suggestions. We believe these suggestions have helped in improving the readability of the manuscript.

Author information

Authors and Affiliations

  1. Dept. of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India, 208 016

    Jay Mahadeokar & Sanjeev Saxena

Authors
  1. Jay Mahadeokar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjeev Saxena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanjeev Saxena.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahadeokar, J., Saxena, S. Faster algorithm to find anti-risk path between two nodes of an undirected graph. J Comb Optim 27, 798–807 (2014). https://doi.org/10.1007/s10878-012-9553-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-012-9553-0

Keywords

Search

Navigation