Static Interconnection Networks
Static Interconnection Networks. CEG 4131 Computer Architecture III Miodrag Bolic. Linear Array. Ring. Ring arranged to use short wires. Linear Arrays and Rings. Linear Array Asymmetric network Degree d=2 Diameter D=N-1 Bisection bandwidth: b=1
Static Interconnection Networks
E N D
Presentation Transcript
Static Interconnection Networks CEG 4131 Computer Architecture III Miodrag Bolic
Linear Array Ring Ring arranged to use short wires Linear Arrays and Rings • Linear Array • Asymmetric network • Degree d=2 • Diameter D=N-1 • Bisection bandwidth: b=1 • Allows for using different sections of the channel by different sources concurrently. • Ring • d=2 • D=N-1 for unidirectional ring or for bidirectional ring
Ring • Fully Connected Topology • Needs N(N-1)/2 links to connect N processor nodes. • Example • N=16 -> 136 connections. • N=1,024 -> 524,288 connections • D=1 • d=N-1 • Chordal ring • Example • N=16, d=3 -> D=5
Multidimensional Meshes and Tori • Mesh • Popular topology, particularly for SIMD architectures since they match many data parallel applications (eg image processing, weather forecasting). • Illiac IV, Goodyear MPP, CM-2, Intel Paragon • Asymmetric • d= 2k except at boundary nodes. • k-dimensional mesh has N=nk nodes. • Torus • Mesh with looping connections at the boundaries to provide symmetry. 3D Cube 2D Grid
Trees • Diameter and ave distance logarithmic • k-ary tree, height d = logk N • address specified d-vector of radix k coordinates describing path down from root • Fixed degree • Route up to common ancestor and down • Bisection BW?
Trees (cont.) • Fat tree • The channel width increases as we go up • Solves bottleneck problem toward the root • Star • Two level tree with d=N-1, D=2 • Centralized supervisor node
Hypercubes • Each PE is connected to (d = log N) other PEs • d = log N • Binary labels of neighbor PEs differ in only one bit • A d-dimensional hypercube can be partitioned into two (d-1)-dimensional hypercubes • The distance between Pi and Pj in a hypercube: the number of bit positions in which i and j differ (ie. the Hamming distance) • Example: • 10011 01001 = 11010 • Distance between PE11 and PE9 is 3 100 110 000 010 111 101 001 011 0-D 1-D 2-D 3-D 4-D 5-D *From Parallel Computer Architectures; A Hardware/Software approach, D. E. Culler
Hypercube routing functions • Example Consider 4D hypercube (n=4) Source address s = 0110 and destination address d = 1101 Direction bits r = 0110 1101 = 1011 1. Route from 0110 to 0111 because r = 1011 2. Route from 0111 to 0101 because r = 1011 3. Skip dimension 3 because r = 1011 4. Route from 0101 to 1101 because r = 1011
k-ary n-cubes • Rings, meshes, torii and hypercubes are special cases of a general topology called a k-ary n-cube • Has n dimensions with k nodes along each dimension • An n processor ring is a n-ary 1-cube • An nxn mesh is a n-ary 2-cube (without end-around connections) • An n-dimensional hypercube is a 2-ary n-cube • N=kn • Routing distance is minimized for topologies with higher dimension • Cost is lowest for lower dimension. Scalability is also greatest and VLSI layout is easiest.
Cube-connected cycle • d=3 • D=2k-1+ • Example N=8 • We can use the 2CCC network
References • Advanced Computer Architecture and Parallel Processing, by Hesham El-Rewini and Mostafa Abd-El-Barr, John Wiley and Sons, 2005. • Advanced Computer Architecture Parallelism, Scalability, Programmability, by K. Hwang, McGraw-Hill 1993.
