[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

On the second point-to-point undirected shortest simple path problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We address the determination of the second point-to-point shortest simple path in undirected networks. The effective reduced cost concept is introduced to compute the second best solution. This concept is used to prove that a path tree containing the second point-to-point shortest simple path is adjacent to any shortest path tree. Therefore, this result immediately implies a method requiring O(m) time once that the shortest path tree is obtained on an undirected network with n nodes and m edges.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahuja R., Magnanti T., Orlin J.B.: Network Flows. Prentice-Hall Inc., Englewood Cliffs (1993)

    MATH  Google Scholar 

  2. Dijkstra E.W.: A note on two problems in connection with graphs. Numer. Math. 1, 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eppstein D.: Finding the K shortest paths. SIAM J. Comput. 28, 653–674 (1999)

    Google Scholar 

  4. Eppstein, D.: http://www.ics.edu/~eppstein/bibs/kpath.bib

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

    Article  MathSciNet  Google Scholar 

  6. Hershberger J., Maxel M., Suri S.: Finding the k shortest simple paths: a new algorithm and its implementation. ACM Trans. Algorithms 3, 4 (2007)

    Article  MathSciNet  Google Scholar 

  7. Katoh N., Ibaraki T., Mine H.: An efficient algorithm for K shortest simple paths. Networks 12, 411–427 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  8. Krasikov I., Noble S.D.: Finding next-to-shortest paths in a graph. Inf. Process. Lett. 92, 117–119 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pettie S., Ramachandran V.: A shortest path algorithm for real-weighted undirected graphs. SIAM J. Comput. 34(6), 1398–1431 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Thorup M.: Undirected single-source shortest paths with positive integer weights in linear time. J. ACM 46, 362–394 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística, Investigación Operativa y Computación Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    Antonio Sedeño-Noda & Carlos González-Martín

Authors
  1. Antonio Sedeño-Noda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos González-Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Sedeño-Noda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sedeño-Noda, A., González-Martín, C. On the second point-to-point undirected shortest simple path problem. Optim Lett 7, 1875–1881 (2013). https://doi.org/10.1007/s11590-012-0528-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-012-0528-y

Keywords

Search

Navigation