Abstract
A class of novel networks called ringtree network is presented in which any ringtree of n nodes can accommodate an n-node ring and an n-node complete binary tree. Ringtree is optimal in respect of the embeddability of ring and complete binary tree in the sense that it has the lowest degree and the minimum number of communication links and the embeddings have no dilation and expansion. Like a binary tree, it permits a simple and efficient layout which is important in VLSI design.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Annaratone et al. The Warp computer: Architecture, implementation and performance. IEEE Trans. on Comput., C-36(12), 1987.
H. R. Arabnia and M. A. Oliver. A Transputer network for the arbitrary rotation of digitised images. The Computer Journal, 30(5):425–32, 1987.
D. A. Bailey and J. E. Cuny. An efficient embedding of large trees in processor grids. In Proc. of Int. Conf. on Parallel Processing, pages 819–923, August 1986.
S. Borkar et al. iWarp: An integrated solution to high-speed parallel computing. Tech. Rep. CMU-CS-89-104, Comput. Sci. Dept, CMU, January 1989.
B. Chazelle. Computational geometry on a systolic chip. IEEE Trans. on Computers, C-33(9):774–85, 1984.
M. Cosnard and Y. Robert. Systolic Givens factorization of dense rectangular matrices. Int. J. Computer Math., 25:287–98, 1988.
M. A. Bonncelli et al. A VLSI tree machine for relational databases. In Proc. 10th Computer Architecture Symp., pages 67–73, June 1983.
D. Gordon. Efficient embedding of binary trees in VLSI arrays. IEEE Trans. on Computers, C-36(9):1009–18, 1987.
E. Horowitz and A. Zorat. The binary tree as an interconnection network: Applications to multiprocessor systems and VLSI. IEEE Trans. on Comput., C-30(4), 1981.
J. Jarosz and J. R. Jaworowski. Computer tree—The power of parallel computations. The Computer Journal, 29(2):103–8, 1986.
H. T. Kung. The Warp computer: a cost-effective solution to supercomputing. An Annual Report, Comput. Sci. Dept., CMU, 1988.
C. E. Lerserson. Systolic priority queues. In Proc. Caltech Conf. on VLSI, pages 199–214, January 1979.
G. Li and T. F. Coleman. A new method for solving triangular systems on distributed-memory message-passing multiprocessors. SIAM J. Sci. Stat. Comput., 10(2):382–96, 1989.
P. P. Li and A. J. Martin. The Sneptree—A versatile interconnection network. In Proc. of Int. Conf. on Parallel Processing, pages 20–7, 1986.
Y-C. Lin and F-C. Lin. A family of systolic arrays for relational database operation. In Systolic Arrays, W. Moore et al Eds., pages 191–200. Adam Hilger, 1987.
R. Melhem. A systolic accelerator for iterative solution of sparse linear systems. IEEE Trans. on Comput., 38(11):1591–5, 1989.
C. Rieger et al. ZMOB: A. new computing engine for AI. In Proc. 7th IJCAI-81, pages 955–60, 1981.
Y. Robert, B. Tourancheau, and G. Villard. Data allocation strategies for the Gauss and Jordan algorithms on a ring of processors. Inf. Proc. Letters, 31:21–9, 1989.
A. L. Rosenberg. Graph embeddings 1988. Lecture Notes in Computer Science, pages 160–9, 1988.
M. R. Samatham and D. K. Pradhan. The de bruijn multiprocessor network: A versatile parallel processing and sorting network for VLSI. IEEE Trans. on Comput., 38(4):567–81, 1989.
S. J. Stolfo and D. E. Shaw. DADO: A. tree-structured machine architecture for production systems. In Proc. Nat. Conf. on AI AAAI-82, pages 242–6, 1982.
J. Ullman. Computational aspects of VLSI. Computer Science Press, Inc, 1984.
H. Y. Youn and A. D. Singh. On implementing large binary tree architectures in VLSI and WSI. IEEE Trans. on Comput., 38(4):526–37, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xie, X., Ge, Y. (1991). An optimal structure that accommodates both a ring and a binary tree. In: Bode, A. (eds) Distributed Memory Computing. EDMCC 1991. Lecture Notes in Computer Science, vol 487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032937
Download citation
DOI: https://doi.org/10.1007/BFb0032937
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53951-3
Online ISBN: 978-3-540-46478-5
eBook Packages: Springer Book Archive