Advertisement

Combinatorica

, Volume 5, Issue 1, pp 57–65 | Cite as

Linear verification for spanning trees

  • J. Komlós
Article

Abstract

Given a rooted tree with values associated with then vertices and a setA of directed paths (queries), we describe an algorithm which finds the maximum value of every one of the given paths, and which uses only
$$5n + n\log \frac{{\left| A \right| + n}}{n}$$
comparisons.

This leads to a spanning tree verification algorithm usingO(n+e) comparisons in a graph withn vertices ande edges.

No implementation is offered.

AMS subject classification (1980)

68 F. 10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Cheriton andR. E. Tarjan, Finding Minimum Spanning Trees,SIAM J. on Computing,5 (1976), 724–742.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Fredman andR. E. Tarjan,private communication, December 1983.Google Scholar
  3. [3]
    R. L. Graham, A. C. Yao, andF. F. Yao, Information Bounds are Weak in the Shortest Distance Problem,JACM,27 (1980), 428- 444.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    D. Harel, A Linear Time Algorithm for the Lowest Common Ancestors Problem,Proc. 21st Annual Symp. on Foundations of Computer Science, (1980), 308–319.Google Scholar
  5. [5]
    R. E. Tarjan, Application of Path Compression on Balanced Trees,JACM,26 (1979), 690–715.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A. C. Yao, AnO(|E| log log |V|) Algorithm for Finding Minimum Spanning Trees,Information Processing Letters,4 (1975), 21–23.zbMATHCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • J. Komlós
    • 1
    • 2
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  2. 2.University of California, San DiegoLa JollaU.S.A.

Personalised recommendations