An optimal parallel minimax tree algorithm

An log n time n/log n processor CREW PRAM algorithm to construct an alphabetic minimax tree is presented. The algorithm achieves these optimal bounds by a combination of existing parallel techniques (applied in novel ways) and a new technique, called accelerated valley filling. Parallel algorithms for several other versions of the minimax tree problem are also discussed.<<ETX>>

[1]  H. James Hoover,et al.  Bounding Fan-out in Logical Networks , 1984, JACM.

[2]  David G. Kirkpatrick,et al.  A Simple Parallel Tree Contraction Algorithm , 1989, J. Algorithms.

[3]  Richard Cole,et al.  Parallel merge sort , 1988, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[4]  Martin Charles Golumbic.  Combinatorial Merging , 1976, IEEE Transactions on Computers.

[5]  D. Huffman.  A Method for the Construction of Minimum-Redundancy Codes , 1952 .

[6]  Mikhail J. Atallah,et al.  Constructing trees in parallel , 1989, SPAA '89.

[7]  Gary L. Miller,et al.  Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits , 1988, SIAM J. Comput..

[8]  Richard Cole,et al.  Approximate and exact parallel scheduling with applications to list, tree and graph problems , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[9]  T. C. Hu.  A New Proof of the T-C Algorithm , 1973 .

[10]  Uzi Vishkin,et al.  Highly parallelizable problems , 1989, STOC '89.

[11]  David A. Huffman,et al.  A method for the construction of minimum-redundancy codes , 1952, Proceedings of the IRE.

[12]  Maria M. Klawe,et al.  Alphabetic Minimax Trees of Degree at Most t , 1986, SIAM J. Comput..

[13]  Gary L. Miller,et al.  Parallel tree contraction and its application , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[14]  Uzi Vishkin,et al.  Finding the maximum, merging and sorting in a parallel computation model , 1981, CONPAR.

[15]  David G. Kirkpatrick,et al.  Alphabetic Minimax Trees , 1985, SIAM J. Comput..

[16]  Lawrence L. Larmore,et al.  Parallel construction of trees with optimal weighted path length , 1991, SPAA '91.