Embedding complete k-ary Trees into 2-dimensional meshes and tori
We have designed an algorithm for embedding of complete k-ary trees into 2-dimensional square meshes. The embedding has load 1, optimal dilation (the constant is 3 if k = 3 and 2 otherwise), and expansion 2. This solution can be easily converted into an embedding with optimal expansion ½ for load 2 while keeping the dilation the same.
Keywordscomplete k-ary tree 2-dimensional square mesh embedding problem expansion load dilation
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- 1.M. J. Fischer and 1V1. S. Paterson. Optimal tree layout. In Proceedings of the 12th ACM Symposium on the Theory of Computing, pages 177–189, 1980.Google Scholar
- 2.D. Gordon. Efficient embeddings of binary trees in VLSI arrays. IEEE Transactions on Computers, C-36:1009–1018, 1987.Google Scholar
- 3.R. Heckmann, R. Klasing, B. Monien, and W. Unger. Optimal embedding of complete binary trees into lines and grids. In Proceedings of Graph-Theoretic Concepts in Computer Science, number 570 in Lecture Notes of Computer Science, pages 25–35. Springer Verlag, 1991.Google Scholar
- 4.M. S. Paterson, W. L. Ruzzo, and L. Snyder. Bounds on minimax edge length for complete binary trees. In Proceedings of the 13th ACM Symposium on the Theory of Computing, pages 293–399, 1981.Google Scholar
- 5.A. D. Singh and H. Y. Youn. Near optimal embedding of binary tree architectures in VLSI. In Proceedings of the 8th International Conference on Distributed Computing Systems, pages 86–93, 1988.Google Scholar
- 6.J. Trdlička and P. Tvrdík. Embedding complete k-ary trees into 2-dimensional meshes and tori. Technical report, Dept. of CS&E, Czech Technical University, Prague, To be published.Google Scholar
- 7.J. D. Ullman. Computational aspects of VLSI. Computer Science Press, 1984.Google Scholar
- 8.P. Zienicke. Embedding of treelike graphs into 2-dimensional meshes. In Proceedings of the Conference on the Graph Theoretical Concepts in Computer Science, number 484 in Lecture Notes of Computer Science, pages 182–192. 1990.Google Scholar