DIMENSION-ORDER ROUTING
Dimension-order routing on the hypercube is essentially a
generalized version of the
greedy row-first routing on the 2D mesh. In row-first
routing, we adjust the column number
or Dimension 1 of the message until it is aligned with
MODIFIED AND GENERALIZED
HYPERCUBES
The versatility and rich algorithmic and theoretical
properties of the hypercube have led
researchers define modified, augmented, generalized, or
hierarchical versions of the
network. We postpone a discussion of hierarc
ADAPTIVE AND FAULTTOLERANT ROUTING
Because there are up to q node-disjoint and edge-disjoint
shortest paths between any
node pairs in a q-cube, it is possible to route messages
around congested nodes/links or in
spite of node and/or link faults. Such adap
BROADCASTING ON A
HYPERCUBE
A simple flooding scheme can be used for broadcasting a
message from one node to
all nodes in a q-cube in q steps, provided that each node
can send a message simultaneously
to all q neighbors (the all-port communication model).
BUTTERFLY AND PERMUTATION
NETWORKS
In Section 14.4, we defined the butterfly network with 2q
nodes and q + 1 columns as
an unfolded q-cube in order to facilitate the discussion,
visualization, and analysis of
hypercube routing algorithms. However, a butte
PLUS-OR-MINUS-2i NETWORK
a plus-or-minus-2i (PM2I) network with eight nodes (p = 2q
nodes
in general) in which each Node x is connected to every node
whose label is x 2i mod p for
some i. It is easy to see that the PM2I network is a
supergraph of the hype
STAR AND PANCAKE NETWORKS
A possible compromise is to construct a network with
sublogarithmic, but nonconstant, node
degree. Such constructions may lead to a network whose
node degree does not grow as fast
as that of a hypercube, while still providing goo
PERFORMANCE PARAMETERS
FOR NETWORKS
In our discussions of various architectures thus far, we
have taken the network diameter
as an indicator of its communication latency. However,
network diameter, though important,
does not always provide an accurate mea
SHUFFLE AND SHUFFLE
EXCHANGE NETWORKS
A perfect shuffle, or simply shuffle, connectivity is one that
interlaces the nodes in a way
that is similar to a perfect shuffle of a deck of cards. That
is, Node 0 is connected to 0, Node
1 to 2, Node 2 to 4, . . .
THE CUBE-CONNECTED CYCLES
NETWORK
The cube-connected cycles (CCC) network can be derived
from a wrapped butterfly as
follows. Remove the pair of cross links that connect a pair
of nodes in Column i 1 to the
same two nodes in Column i and instead connect t