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The Computer Journal Advance Access published online on June 13, 2007
The Computer Journal, doi:10.1093/comjnl/bxm027
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Parallel Generation Of t-ary Trees in A-order

H. Ahrabian1,2,* and A. Nowzari-Dalini1,2

1 Center of Excellence in Biomathematics, School of Mathematics, Statistics, and Computer Science, University of Tehran, Tehran, Iran
2 Institute for Studies in Theoretical Physics and Mathematics (I.P.M.), Tehran, Iran

* Corresponding author: ahrabian{at}ut.ac.ir

Received 24 August 2006; revised 11 February 2007

Accepted for publication 26 April 2007.

We present a cost-optimal and adaptive parallel algorithm for generating t-ary trees in A-order. The generation is based on an encoding using integer sequences (z-sequences) due to Zaks [(1980), Lexicographic generation of ordered tree. Theor. Comput. Sci., 10, 63–82]. Our algorithm is the first introduced parallel generation algorithm, which generates t-ary trees in A-order in the literature. The used computational model is CREW SM SIMD multi-processors. This algorithm is designed based on a novel sequential generation algorithm that is also discussed. Ranking and unranking algorithms for z-sequences are also presented.

Key Words: G.2.1 Combinatorial Algorithm • G.2.2 Graph Theory (Trees)


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