A Mesh interconnection network provides point-to-point communication links with each processor to every other processor in the network. Mesh interconnection networks provide redundancy, in the information sending or receiving of a communication link failure, meshed networks enable data to be routed through any other site connected to the network. Because each processor has a point-to-point connection link to every other processors, mesh interconnection are the most expensive and difficult to maintain.
In a d-dimensional d√p × d√p × . . . . × d√p mesh, the p processors may be thought of as logically arranged in a d-dimensional d√p × d√p × . . . . × d√p array. The processor at location (id-i, id-2 , i0) of the array is connected to the processors at locations (id-l , .. . , ij ± 1,… ,i 0), 0 < j < d – 1. This network has degree 2d, diameter d(d√p – 1) and a p1 – 1/d bisector. It can perform permutations in θ(d d√p) cycles.
2 dimension mesh interconnection network Characteristics:
- A 2-Dimensional mesh can be laid out in 2-Dimension space, making it attractive from a wiring standpoint.
- A k-dimensional mesh with N = nk (n is the rank mash) nodes has an interior node degree of 2k and the network diameter is k(n-1). So, pure mesh network is asymmetric.
- The communication is allowed only in between neighboring nodes; hence interior nodes communicate with 2k other processors.
- Mesh interconnection network has one another variant named as an Illiac mash whose topology is equivalent to a chordal ring of degree 4. In general, an n × n Illiac mash should have a diameter of d= n – 1, which only half of the diameter for a pure mesh.
- 2-dimensional meshes can be augmented with wraparound links to form two dimensional Tori.
- The three-dimensional cube is a generalization of the 2-D mesh to three dimensions (each node element in a 3-D cube, with the exception of those on the periphery, is connected to six other nodes, two along each of the three dimensions).
A variety of physical simulations commonly executed on parallel computers (for example, 3-Dimensional weather modeling, structural modeling, etc.) can be mapped naturally to 3-Dimensional network typologies.
Example of 2-dimensional mesh:
Figure: 2-Dimension mesh with rank 4
One of the most natural interconnection schemes is the 2-dimensional mesh shown in above figure is an extension of the linear array to two-dimensions. Each dimension has √p nodes i.e. (√p × √p mesh) with a node identified by a two-tuple (i, j). Its physical layout is straightforward in the 2-dimensional space.
The degree of the 2-dimensional mesh interconnection network is = 4.
And the diameter of the 2-dimensional mesh interconnection network is = 2(√p – 1) and
a bisector of of the 2-dimensional mesh interconnection network is = √p
It performs permutations in θ(√p) cycles.
Consider the mash represent in above figure:
The rank of the mash n = 4
The dimension of the mash k = 2
The total number of nodes in the mash N = nk = 42 = 16
The degree of interior node is = 2 × k = 2 × 2 = 4
The diameter is = k × (n – 1) = 2 × (4 – 1) = 2 × 3 = 6
In 2-dimension mesh interconnection network every node is connected to four other nodes whose indices differ in any dimension by one.
Figure: 3-D Mesh Connected Interconnection Network
Consider the 3-Dimension mash represent in above figure:
The rank of the mash n = 3
The dimension of the mash k = 3
The total number of nodes in the mash N = nk = 33 = 27
The degree of interior node is = 2 × k = 2 × 3 = 6
The diameter is = k × (n – 1) = 3 × (3 – 1) = 3 × 2 = 6
Advantages of mesh interconnection network:
- Each communication link in the network can carry its own data load.
- Information has access to fastest paths and can load balance.
- This network provides redundancy and fault tolerance between processes and ensures the best possibility that the network is always available.
Disadvantages of mesh interconnection network:
- Uses bulk communication links to implement mesh interconnection networks.
- Has a high administrative overhead.
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