Bscs Course

1. PARALLEL AND DISTRIBUTED COMPUTING
INTERCONNECTION TOPOLOGIES

2. NETWORK TOPOLOGIES
Two types of topologies
 Shared Network: Communicate at most one message at a
time that’s why limited scalability
 Switched Network: Simultaneously transfer several messages
between different pairs of nodes.

3. NETWORK TOPOLOGIES
 Degree: Maximum number of neighbors of any node
 Diameter: length of longest of all shortest path
 BisectionWidth: minimum number of edges(links) to be
removed to disconnect the network into two halves. In case of
odd number of nodes one half can include one more node.

4. NETWORK TOPOLOGIES
 Constant Degree: Should be constant i.e. independent of
network size.This property allows scale large number of nodes
without adding excessive number of connections.
 Low Diameter: Should be minimum in order to provide
efficient communication between any pair of nodes
 High BisectionWidth: low bisection width can slow down
communication and thus limit the performance of applications.

6. NETWORK TOPOLOGIES
 Linear Array
 2D Mesh/torus
 3D Mesh/torus
 BinaryTree
 Hypercube

7. LINEAR ARRAY
 Every node is connected to left and its right neighbor and thus
degree is 2 i.e. deg(Ln)=2
 Longest distance between any two nodes is between leftmost
node and the right most node i.e. Diam(Ln)=n-1
 Bisection width is one i.e. BW(Ln)=1, Since only one link
between P(n-1)/2 and P(n/2) needs to be removed in order to split
into two disconnected halves.

8. 2D MESHTOPOLOGY
 Nodes are arranged in a (usually
square) grid
 Each node has most four neighbors i.e.
deg(M4,4)=√n=4
 Longest distance between P0,0 and P3,3
Leading to diameter of 6 i.e.
Daim(Mk,k)=2(√n-1)=6.
 Removing all links between second
and third row/column disconnects
M4,4 into equal halves.Thus bisection
width is bw(Mk,k)=(√n =4)

9. 2D TORUSTOPOLOGY
 A frequently used extension of mesh is torus
 2D Torus Tk,k is extends Mk,k by adding wrap-around
edges to directly connect left and right node of each
raw as well the bottom and top node of each
column.
 Each node has most four neighbors i.e. deg(M4,4)=4
 Longest distance between P0,0 and P3,3 Leading to
diameter of 6 i.e. Daim(Mk,k)=(√n-1)=3.
 Removing all links between second and third
row/column disconnects M4,4 into equal halves.Thus
bisection width is bw(Mk,k)=(2√n = 8)

10. 3D MESHTOPOLOGY
 Nodes are arranged in a (usually
square) grid
 Each node has most six neighbors
i.e. degree is Deg(Mk,k,k)=6
 Longest distance between P0,0 and
P3,3 Leading to diameter of 6 i.e.
Daim(Mk,k,k)=3(3√n-1).
 Bisection width can be calculated as
BW(Mk,k)=( n2/3)

11. 3D MESHTOPOLOGY
 3D Mesh topology has many desirable features such as a
constant degree, relatively low diameter, and relatively high
bisection width.
 Thus it has been used as an interconnection network in top
supercomputers

12. 3D TORUSTOPOLOGY
 Nodes are arranged in a (usually
square) grid
 Similar to 3d-Mesh topology just by
adding wrap-around edges

13. BINARY TREE TOPOLOGY
 In order to reduce network diameter, a tree based structure can be
used.
 Each node is connected to its parent and two Childs hence degree
is deg(BTd)=3
 The longest distance is when travelling between left most node to
right most half of tree, which requires growing up to the root and
then down again so Diam(BTd) = 2(d-1) = 2log2 (n+1).
 In-spite of constant degree and diameter is low disadvantage of
binary tree is its bisection width.

14. BINARY TREE TOPOLOGY
 Removing only a single link
with the root, we can split
the network into two
disconnected components
i.e. bitwise width bw(BTd)=1

15. HYPERCUBE NETWORK TOPOLOGY
 Hypercube network can be
represented as a graph with
n=2d nodes that has each
vertex labeled with a distinct
bit of length d
 Vertices that are connected iff
bits string differ in exactly one
bit.

17. HYPERCUBE NETWORK TOPOLOGY
 Each node is connected to d
other nodes so degree will
deg(Qd)=d=log2(n)
 Longest distance between two
nodes diam(Qd)=d=log2(n)
 Removing all links between nodes
starting with label O and all
nodes starting with 1
disconnects Hd into two halves
i.e. it holds bw(Qd)=n/2

18. NETWORK TOPOLOGY

19. HYPERCUBE NETWORK TOPOLOGY
 Overall hypercube has the highest bisection width
 Furthermore diameter is very low (logarithmic)
 But disadvantage is non constant degree. i.e. number of required
links per node is logarithmic
 Making it difficult to scale up to large number of nodes.