Skip to main content
SpringerLink
Log in

Searching among intervals and compact routing tables

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Shortest paths in weighted directed graphs are considered within the context of compact routing tables. Strategies are given for organizing compact routing tables so that extracting a requested shortest path will takeo(k logn) time, wherek is the number of edges in the path andn is the number of vertices in the graph. The first strategy takesO (k+logn) time to extract a requested shortest path. A second strategy takes Θ(k) time on average, assuming alln(n−1) shortest paths are equally likely to be requested. Both strategies introduce techniques for storing collections of disjoint intervals over the integers from 1 ton, so that identifying the interval within which a given integer falls can be performed quickly.

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

Similar content being viewed by others

References

  1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman.The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Massachusetts, 1974.

    Google Scholar 

  2. T. H. Cormen, C. E. Leiserson, and R. L. Rivest.Introduction to Algorithms. McGraw-Hill, New York, 1990.

    Google Scholar 

  3. N. Deo and C. Pang. Shortest-path algorithms: taxonomy and annotation.Networks, 14:275–323, 1984.

    Google Scholar 

  4. E. W. Dijkstra. A note on two problems in connexion with graphs.Numer. Math., 1:269–271, 1959.

    Google Scholar 

  5. H. N. Djidjev, G. E. Pantziou, and C. D. Zaraliagis. Computing shortest paths and distances in planar graphs.Proceedings of the International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, Vol. 510, pp. 327–338. Springer-Verlag, Berlin, 1991.

    Google Scholar 

  6. R. W. Floyd. Algorithm 97: shortest path.Comm. ACM, 5:345, 1962.

    Google Scholar 

  7. G. N. Frederickson. Implicit data structures for the dictionary problem.J. Assoc. Comput. Mach., 30:80–94, 1983.

    Google Scholar 

  8. G. N. Frederickson. Implicit data structures for weighted elements.Inform. and Control, 66:61–82, 1985.

    Google Scholar 

  9. G. N. Frederickson. Fast algorithms for shortest paths in planar graphs, with applications.SIAM J. Comput., 16:1004–1022, 1987.

    Google Scholar 

  10. G. N. Frederickson. Planar graph decomposition and all pairs shortest paths.J. Assoc. Comput. Mack., 38:162–204, 1991.

    Google Scholar 

  11. G. N. Frederickson. Searching among intervals and compact routing tables.Proceedings of the International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, Vol. 709, pp. 28–39. Springer-Verlag, Berlin, 1993.

    Google Scholar 

  12. G. N. Frederickson. Using cellular embeddings in solving all pairs shortest paths problems.J. Algorithms, 19:45–85, 1995.

    Google Scholar 

  13. G. N. Frederickson and R. Janardan. Designing networks with compact routing tables.Algorithmica, 3:171–190, 1988.

    Google Scholar 

  14. M. L. Fredman. New bounds on the complexity of the shortest path problem.SlAM J. Comput., 5:83–89, 1976.

    Google Scholar 

  15. M. L. Fredman, J. Komlos, and E. Szemeredi. Storing a sparse table withO(1) worst case access.J. Assoc. Comput. Mach., 31:538–544, 1984.

    Google Scholar 

  16. M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms.J. Assoc. Comput. Mach., 34:596–615, 1987.

    Google Scholar 

  17. F. Harary.Graph Theory. Addison-Wesley, Reading, Massachusetts, 1969.

    Google Scholar 

  18. J. I. Munro and H. Suwanda. Implicit data structures for fast search and update.J. Comput. System Sci., 21:236–250, 1980.

    Google Scholar 

  19. N. Santoro and R. Khatib. Labelling and implicit routing in networks.Comput. J., 28:5–8, 1985.

    Google Scholar 

  20. R. E. Tarjan and A. C.-C. Yao. Storing a sparse table.Comm. ACM, 21:606–611, 1979.

    Google Scholar 

  21. P. Van Emde Boas, R. Kaas, and E. Zijlstra. Design and implementation of an efficient priority queue.Math. Systems Theory, 10:99–127, 1977.

    Google Scholar 

  22. J. van Leeuwen and R. B. Tan. Computer networks with compact routing tables. In G. Rozenberg and A. Salomaa, editors,The Book of L, pp. 259–273. Springer-Verlag, New York, 1986.

    Google Scholar 

  23. S. Warshall. A theorem on boolean matrices.J. Assoc. Comput. Mach., 9:11–12, 1962.

    Google Scholar 

  24. D. E. Willard. Log-logarithmic worst-case range queries are possible in space Θ(n).Inform. Process. Lett., 17:81–84, 1983.

    Google Scholar 

  25. A. C.-C. Yao. Should tables be sorted?J. Assoc. Comput. Mach., 28:615–628, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Purdue University, 47907, West Lafayette, IN, USA

    G. N. Frederickson

Authors
  1. G. N. Frederickson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by C. K. Wong.

This research was supported in part by the National Science Foundation under Grants CCR-9001241 and CCR-9322501 and by the Office of Naval Research under Contract N00014-86-K-0689.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frederickson, G.N. Searching among intervals and compact routing tables. Algorithmica 15, 448–466 (1996). https://doi.org/10.1007/BF01955044

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01955044

Key words

Search

Navigation