Synchronizing Large VLSI Processor Arrays
IEEE Transactions on Computers
Topological Properties of Hypercubes
IEEE Transactions on Computers
Interconnection networks for large-scale parallel processing: theory and case studies (2nd ed.)
Interconnection networks for large-scale parallel processing: theory and case studies (2nd ed.)
Performance of Synchronous and Asynchronous Schemes for VLSI Systems
IEEE Transactions on Computers
Properties of Generalized Branch and Combine Clock Networks
IEEE Transactions on Parallel and Distributed Systems
Clocking Arbitrarily Large Computing Structures Under Constant Skew Bound
IEEE Transactions on Parallel and Distributed Systems
Comparison of tree and straight-line clocking for long systolic arrays
ICASSP '91 Proceedings of the Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference
On the Complexity of Designing Optimal Branch-and-Combine Clock Networks
IEEE Transactions on Computers
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Branch-and-Combine (BaC) clock distribution has recently been introduced. The most interesting aspect of the new scheme is its ability to bound skew by a constant irrespective of network size. In this paper, we introduce algorithms for systematic synthesis of BaC networks for clocking meshes, tori, and hypercubes of different dimensionalities. For meshes our approach relies on tiling techniques. We start with the identification of basic proper tiles satisfying certain criteria. We define a set of valid transformations on tiles. By appropriately applying a sequence of transformations on a basic proper tile, one could synthesize a valid BaC network. We formally introduce methods and procedures for applying the above steps to systematically construct different valid BaC network designs for 2D and 3D meshes. To construct BaC networks for clocking hypercubes of any dimensionality we describe a formal methodology. In this case, we utilize an approach called replication which is based on constructing larger hypercube clocking networks from smaller ones. We combine the techniques for 2D, 3D meshes with replication techniques to formulate a methodology applicable to meshes and tori of dimensionality greater than three.We provide proofs of correctness for the algorithms we introduce. Besides, we formally define an optimality criterion based on link costs which is utilized to check the optimality of the synthesized network designs. In the case of meshes, we show that the majority of synthesized networks are optimal with respect to our defined criterion. For those suboptimal networks, we describe a procedure for identifying and removing unnecessary (redundant) links. The procedure is guaranteed to optimize the network without changing its behavioral parameters.