An optimal parallel algorithm to reconstruct a binary tree from its traversals

  • Stephan Olariu
  • Michael Overstreet
  • Zhaofang Wen
Parallel Processing And Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 497)


We consider the following problem. For a binary tree T=(V,E) where V={1, 2,...,n}, given its inorder traversal and either its preorder traversal or it postorder traversal, reconstruct the binary tree. We present a new parallel algorithm for this problem. Our algorithm requires O(n) space. The main idea of our algorithm is to reduce the reconstruction process to parallel merging. With the best results for parallel merging, our algorithm can be implemented in O(logn) time using O(n/logn) processors on the EREW PRAM, or in O(loglogn) time using O(n/log logn) processors on the CREW PRAM. Consequently, an ordered tree can be reconstructed from its preorder and postorder traversals. Our results improve the best previous results for this problem in literature either in cost or in the model of computation.


Algorithms Binary trees Ordered trees PRAM Parallel algorithms Traversals 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Stephan Olariu
    • 1
  • Michael Overstreet
    • 1
  • Zhaofang Wen
    • 1
  1. 1.Department of Computer ScienceOld Dominion UniversityNorfolkUSA

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