An Area Lower Bound for a Class of Fat-Trees (Extended Abstract)

A graph-theoretic definition is proposed to make precise the sense in which a “fat-tree” is a tree-like interconnection of subnetworks whose bandwidth is adequately described by the capacity of the channels between subnetworks. The definition is shown to encompass a number of known networks such as the concentrator fat-tree, the pruned butterfly, and the tree-of-meshes. In the established framework, a non-trivial Ω(N log2N) lower bound is derived for the area of a class of fat-trees, with implications for their area-universality.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  Bruce M. Maggs,et al.  Universal packet routing algorithms , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[3]  Charles E. Leiserson,et al.  Fat-trees: Universal networks for hardware-efficient supercomputing , 1985, IEEE Transactions on Computers.

[4]  Ronald I. Greenberg.  The fat-pyramid: a robust network for parallel computation , 1990 .

[5]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[6]  Charles E. Leiserson,et al.  Randomized Routing on Fat-Trees , 1989, Adv. Comput. Res..

[7]  Paul Edwin Bay.  Area-universal interconnection networks for VLSI parallel computers , 1992 .

[8]  Kurt Mehlhorn,et al.  A Lower Bound for Area-Universal Graphs , 1994, Inf. Process. Lett..

[9]  Frank Thomson Leighton,et al.  A Framework for Solving VLSI Graph Layout Problems , 1983, J. Comput. Syst. Sci..

[10]  C. Thomborson,et al.  A Complexity Theory for VLSI , 1980 .

[11]  G. Bilardi,et al.  Deterministic on-line routing on area-universal networks , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[12]  Paul Bay,et al.  An area-universal VLSI circuit , 1993 .

[13]  W. Daniel Hillis,et al.  The network architecture of the Connection Machine CM-5 (extended abstract) , 1992, SPAA '92.