MESHES AUGMENTED WITH
NONLOCAL LINKS
Because one of the major drawbacks of low-dimensional
meshes and tori is their rapidly
increasing diameters when the number of processors
becomes large, it has bee
MESHES OF TREES
The mesh of trees architecture represents another attempt
at combining the advantages
of tree and mesh structures. Like the pyramid, an l-level
mesh of trees architecture has a
2 l 1 2
PYRAMID AND MULTIGRID
SYSTEMS
The pyramid architecture combines 2D mesh and tree
connectivities in order to gain
advantages from both schemes. Topologically, the pyramid
inherits low logarithmic diame
MESHES WITH DYNAMIC LINKS
There are various ways of designing meshes so that node
connectivities can change
dynamically. For example, if buses are segmented through
the insertion of switches that can
HYPERCUBES AND THEIR
ALGORITHMS
DEFINITION AND MAIN PROPERTIES
The origins of the hypercube architecture can be traced
back to the early 1960s [Squi63].
Subsequently, both the direct (single-stage) ve
EMBEDDINGS AND THEIR
USEFULNESS
Given the architectures A and A' we embed A into A' by
specifying
A node mapping (indicating that Node v of A is mapped
onto Node v' of A'); the node
mapping can be ma
ROUTING PROBLEMS ON A
HYPERCUBE
Intuitively, hypercubes should perform better in dealing
with routing problems than 2D
meshes, because their larger node degree translates to the
availability of more a
BITONIC SORTING ON A HYPERCUBE
If we sort the records in the lower (xq1 = 0) and upper
(xq1 = 1) subcubes in opposite
directions, the resulting sequence in the entire cube will be
bitonic. Now the shi
DEFINING THE SORTING PROBLEM
The general problem of sorting on a hypercube is as
follows: Given n records distributed
evenly among the p = 2q processors of a q-cube (with each
processor holding n/p re
EMBEDDING OF ARRAYS AND TREES
In this section, we show how meshes, tori, and binary trees
can be embedded into
hypercubes in such a way as to allow a hypercube to run
mesh, torus, and tree algorithms