A parallel algorithm for path-min queries in trees

  • Sung Kwon Kim
Computer Architecture, Concurrency, Parallelism, Communication And Networking
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)


Given a rooted tree T on n vertices with each vertex v having a label cost(v), preprocess T so that, given a pair of vertices v, w, the minimum-cost vertex on the path between v and w (the path-min of v and w) can be found efficiently. We give a preprocessing algorithm running in O(log n) time using O(n) processors in the CREW PRAM. After preprocessing, a path-min query can be answered in O(log n) time using a single processor.


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  1. [1]
    K. Abrahamson, N. Dadoun, D.G. Kirkpatrick and T. Przytycka, A simple parallel tree contraction algorithm, J. Algorithms, 10, 287–302 (1989).Google Scholar
  2. [2]
    R.J. Anderson and G.L. Miller, Deterministic parallel list ranking, Proc. 3rd AWOC. (Lecture Notes in Computer Sciences, vol. 319) 81–90 (1988).Google Scholar
  3. [3]
    R.P. Brent, The parallel evaluation of general arithmetic expressions, J. ACM, 21, 201–206 (1974).Google Scholar
  4. [4]
    O. Berkman, D. Breslauer, Z. Galil, B. Schieber and U. Vishkin, Highly parallelizable problems, Proc. ACM Symp. on Theory of Computing, 309–319 (1989)Google Scholar
  5. [5]
    B. Chazelle, Computing on a free tree via complexity-preserving mappings, Algorithmica, 2, 337–361 (1987).Google Scholar
  6. [6]
    R. Cole and U. Vishkin, Approximate parallel scheduling. Part I: The basic technique with applications to optimal parallel list ranking in logarithmic time, SIAM J. Comput., 17, 128–142 (1988).Google Scholar
  7. [7]
    D. Knuth, The art of programming: Fundamental algorithms, Addison-Wesley, Reading, Mass. (1968).Google Scholar
  8. [8]
    A.A. Schäffer, Optimal node ranking of trees in linear time, Inform. Process. Lett., 33, 91–96 (1989).Google Scholar
  9. [9]
    B. Schieber and U Vishkin, On finding lowest common ancestors: simplification and parallelization, SIAM J. Comput., 17, 1253–1262 (1988).Google Scholar
  10. [10]
    R. Tarjan and U. Vishkin, An efficient parallel biconnectivity algorithm, SIAM J. Comput., 14, 862–874 (1985).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Sung Kwon Kim
    • 1
  1. 1.Department of Computer Science and Engineering, FR-35University of WashingtonSeattle

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