Skip to main content
SpringerLink
Log in

Searching among intervals and compact routing tables

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 700))

Included in the following conference series:

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 take o(k log n) time, where k is the number of edges in the path and n the number of vertices in the graph. The first strategy takes O(k+log n) time to extract a requested shortest path. A second strategy takes O(K/n 2) average time, if all requested paths are equally likely, where K is the total number of edges (counting repetitions) in all n(n}-1) shortest paths. Both strategies introduce techniques for storing collections of disjoint intervals over the integers from 1 to n, 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 chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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. 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 

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

    Google Scholar 

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

    Google Scholar 

  5. E. W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269–271, 1959.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  8. G. N. Frederickson. Implicit data structures for the dictionary problem. J. ACM, 30:80–94, 1983.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  11. G. N. Frederickson. Using cellular embeddings in solving all pairs shortest paths problems. In Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, pages 448–453, 1989. revised version in Burdue University technical report CSD-TR-897, 1992.

    Google Scholar 

  12. G. N. Frederickson. Planar graph decomposition and all pairs shortest paths. J. ACM, 38:162–204, 1991.

    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. SIAM J. on Computing, 5:83–89, 1976.

    Google Scholar 

  15. M. L. Fredman, J. Komlos, and E. Szemeredi. Storing a sparse table with O(1) worst case access. J. ACM, 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. ACM, 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. Computer and System Sciences, 21:236–250, 1980.

    Google Scholar 

  19. N. Santoro and R. Khatib. Labelling and implicit routing in networks. Computer Journal, 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. J. van Leeuwen and R. B. Tan. Computer networks with compact routing tables. In G. Rozenberg and A. Salomaa, editors, The Book of L, pages 259–273. Springer-Verlag, New York, 1986.

    Google Scholar 

  22. S. Warshall. A theorem on boolean matrices. J. ACM, 9:11–12, 1962.

    Google Scholar 

  23. D. E. Willard. Log-logarithmic worst-case range queries are possible in space θ(n). Info. Proc. Lett., 17:81–84, 1983.

    Google Scholar 

  24. A. C.-C. Yao. Should tables be sorted? J. ACM, 28:615–628, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Greg N. Frederickson

Authors
  1. Greg N. Frederickson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Andrzej Lingas Rolf Karlsson Svante Carlsson

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Frederickson, G.N. (1993). Searching among intervals and compact routing tables. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_59

Download citation

  • DOI: https://doi.org/10.1007/3-540-56939-1_59

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56939-8

  • Online ISBN: 978-3-540-47826-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation