M. Umasankar et A. Elamawy, GENERALIZED ALGORITHMS FOR SYSTEMATIC SYNTHESIS OF BRANCH-AND-COMBINECLOCK NETWORKS FOR MESHES, TORI, AND HYPERCUBES, IEEE transactions on parallel and distributed systems, 6(12), 1995, pp. 1283-1300
Citations number
12
Categorie Soggetti
System Science","Engineering, Eletrical & Electronic","Computer Science Theory & Methods
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.