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http://wiki.expertiza.ncsu.edu/index.php/CSC/ECE_506_Spring_2011/ch12#Linear_Array
Ring Topology.png)
Number of Links as function of number of nodes, N : N (linear)
Number of connections per node: 2 (constant)
Link bandwidth = speed of single link, b
Total bandwidth = N * b
Bisection bandwidth = 2 * b (to cut the network in half, you must
cut two links)
Diameter = N / 2
In a ring architecture, all nodes are connected in a ring fashion, as shown in Figure 2. Every node has two neighbors regardless the size of the ring. Its small degree is preferable, but it’s diameter increases linearly with the number of nodes. Its strengths include: (1)cable faults are easily located, which makes troubleshooting easier. (2) Moderately easy to install compared with other architectures. Its limitations include: (1)Expansion to the network can cause network disruption. (2)Even a single break in the cable can disrupt the entire network.
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In a star architecture, assume there are N nodes, N − 1 nodes connect to a center node, as shown in Figure 3. Only the center node has a degree of N − 1. Other nodes have degree of 1. Diameter of a star architecture is 2, regardless its size. Its strengths include: (1) A small diameter means a small average hop distance, which is a favorable characteristic. (2) Simplicity to operate. Each node is isolated free of impact from failed nodes. Its limitations include: (1) Failure of the central node fails the entire network. (2) Central node is the bottleneck.
2-D Mesh.png)
Number of Links as function of number of nodes, N : ~4N (linear) Number of connections per node: 4 (constant) Link bandwidth = speed of single link, L Total bandwidth = 4N * L Bisection bandwidth = sqrt(N) * L Diameter = 2 * sqrt(N) - 2
In a mesh, nodes are connected as a grid, as shown in Figure 4. Expansion is easy for meshes. Little effort is needed when adding more nodes to the existing architecture. Nodes have different degrees according to their locations within the mesh. Corner nodes have degree of 2. Edge nodes have degree of 3. Inner nodes have degree of 4. Its strengths include: (1) Multiple paths between a pair of nodes, tolerant to link failure. (2) Easy to expand. Its limitations include: (1) Diameter can be very large. (2) Irregularity, less bandwidth for nodes at corners and edges.
Complete Connections.png)
Number of Links as function of number of nodes, N : N*(N - 1) / 2
Number of connections per node: N - 1
Link bandwidth = speed of single link, L
Total bandwidth = L * N * (N - 1) / 2
Bisection bandwidth = (N / 2)2 * L
Diameter = 1.png)
d = dimension number of nodes N = 2d
Number of Links as function of number of nodes, N : N * d / 2
= (N log N) / 2
Number of connections per node: d = log N
Link bandwidth = speed of single link, L
Total bandwidth = L * (N log N) / 2
Bisection bandwidth = N / 2
Diameter = d = log N
Cube Connected Cycles.png)
d = dimension number of nodes N = d * 2d
Number of Links as function of number of nodes, N : 3 * N / 2
Number of connections per node: 3
Link bandwidth = speed of single link, L
Total bandwidth = L * 3 * N / 2
Bisection bandwidth = d @ log N
Diameter = 2 * d @ 2 log N
Tree.png)
k = depth number of nodes N = 2k - 1
Number of Links as function of number of nodes, N : 3 * N - 1
Number of connections per node: 3
Link bandwidth = speed of single link, L
Total bandwidth = L *( 3 * N - 1)
Bisection bandwidth = 1 (cut a link to the root)
Diameter = 2 * k - 2 @ 2 log N
In a binary tree, the top node is the root and the bottom nodes are the leaves, as shown in Figure 5. Every node except the root node has two offspring nodes. A node’s children are those nodes that appear immediately beneath the node itself. A node’s parent is the node immediately above it. A tree’s root is the single node that contains no parent. Its strengths include: (1) Supported by many network vendors and even hardware vendors. (2)All the nodes have access to the larger and their immediate networks, best for branched out networks. Its limitations include: (1)Bottleneck on the root node. (2) When the tree is big, it is difficult to configure and can get complicated after a certain point. .png)
In a fat binary tree, only leaves are intellectual properties (IP), as shown in Figure 6. Interior nodes are switches. When moving towards the root node, there are more links between a parent node and a child node. The number of inter-node links increases by order of 2. .png)
In a butterfly architecture, as shown in Figure 7. Basic butterfly networks have two main disadvantages. Firstly, it lacks of path diversity. There is only one path from a source node to a destination node. Secondly, long wires are inevitable. Long wires must transverse half of the diameter of the network. .png)
A torus architecture is obtained by adding direct connections to two end nodes in the same row or column in a mesh architecture. A 16-node torus is shown in Figure 8. Compared with mesh, its diameter is reduced. A regular torus has long wrap-around links. By folding a torus, long wires can be avoided at the cost of doubling the wire length.
