GENERALIZED ALGORITHMS FOR SYSTEMATIC SYNTHESIS OF BRANCH-AND-COMBINECLOCK NETWORKS FOR MESHES, TORI, AND HYPERCUBES

Branch-and-Combine (BaC) clock distribution has recently been introduc ed. The most interesting aspect of the new scheme is its ability to bo und skew by a constant irrespective of network size, In this paper, we introduce algorithms for systematic synthesis of BaC networks for clo cking meshes, tori, and hypercubes of different dimensionalities. For meshes our approach relies on tiling techniques, We start with the ide ntification of basic proper tiles satisfying certain criteria, We defi ne a set of valid transformations on tiles, By appropriately applying a sequence of transformations on a basic proper tile, one could synthe size a valid BaC network, We formally introduce methods and procedures for applying the above steps to systematically construct different va lid BaC network designs for 2D and 3D meshes, To construct BaC network s for clocking hypercubes of any dimensionality we describe a formal m ethodology, In this case, we utilize an approach called replication wh ich is based on constructing Larger hypercube clocking networks from s maller ones. We combine the techniques for 2D, 3D meshes with replicat ion techniques to formulate a methodology applicable to meshes and tor i of dimensionality greater than three. We provide proofs of correctne ss for the algorithms we introduce, Besides, we formally define an opt imality criterion based on link costs which is utilized to check the o ptimality of the synthesized network designs, In the case of meshes, w e show that the majority of synthesized networks are optimal with resp ect to our defined criterion, For those suboptimal networks, we descri be a procedure for identifying and removing unnecessary (redundant) li nks, The procedure is guaranteed to optimize the network without chang ing its behavioral parameters.