The right gure shows second level all to all

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Unformatted text preview: 2B Interconnect Topologies Fall 2013 ' ' ' ' 234#.4#56##&.(+7 809<#=#6&.(*)+,>?#695#.40$=91@#A B0$#@=031.C04=%&.) 2D Torus (k ­ary 2 ­cube)    degree: 4 ! :36;$&    ' () diameter: ( /01)$1 k ­    total links/link bandwidth: ' 234#.4#56##&.7 ' 809<#=#6&.).+ ,    average distance ' >?#695#.40$=91@#A k/2 ' B0$#@=031.C04=%&.() 2k*k    bisecBon bandwidth:    D BisecBon bandwidth is decent But other issues, beyond the scope of this lecture    21 2kB Interconnect Topologies Fall 2013 k ­ary n ­cube    P = k * k * k *…. Or P = k1 * k2 * k3 * ….    Degree = 2n    Diameter = n*k/2    Average Distance = n*k/4    BisecBon Bandwidth = 2B*P/k 22 Interconnect Topologies Fall 2013 MulB ­Ber Networks LL LR D One supernode in the PERCS topology Figure 1: The PERCS network – the left figure shows all to all connections within a supernode (connections originating from only two MulB ­Ber all ­to ­all nodes, 0 and 16, are shown to keep the diagram simple). The right figure shows second-level all to all connections across supernodes (again D links originating from only two supernodes, colored in red, are shown). topologies. Using traces collected by our emulation-based techbetween any two nodes in one hop. To maintain simplicity, LL and 23 Interconnect Topologies Fall 2 nodes, nique, we simulate application runs on hundreds of thousands of LR links originating from only two013 numbered 0 and 16 are cores. Non-uniform link bandwidths on different classes of links shown in Figure 1 (left). Switches and Indirect networks switch node switch switch switch 24 Interconnect Topologies Fall 2013 !"##$ % &'()#*#"+(,-+(.#"(/#+-'$*(,0#+("#+12/("'*3)'04 : 5;("6+*"##<+++3#'/3*+++- 7+12/5 8 % ='>#-+-#/"## 54 % ?2@+A'$#0*'2,+@'-*3 7+9    Slide from a presentation by Prof. Dr.-Ing. Axel Hunger 25 Interconnect Topologies Fall 2013 99 Fat Tree Fatter higher bandwidth links (more connections in reality) Bisection width scales with number of nodes N.    Slide from a presentation by Prof. Dr.-Ing. Axel Hunger 26 Interconnect Topologies Fall 2013 9B BuXerfly For P processors, log p ranks with p switches    Node(i,j) is connected to two nodes with rank i ­1 – node(i ­1,j) and node(i ­1,m) where m is the integer found by flipping the ith most significant bit in binary representaBon of j    Rank 3 verBces can be processors/memory    27 0 1 2 3 4 5 6 7 Rank 0 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 Rank 1 1,0 1,1 1,2 1,3 1,4 1,5 1,6 1,7 Rank 2 2,0 2,1 2,2 2,3 2,4 2,5 2,6 2,7 Rank 3 3,0 3,1 3,2 3,3 3,4 3,5 3,6 3,7 Interconnect Topologies Fall 2013 BuXerfly    RouBng is simple: follow the binary 0 means ship ler;    1 means ship right.       diameter: log P Average distance log P bisecBon: P/2    What is not good?       28 Interconnect Topologies Fall 2013 Omega networks 29 Interconnect Topologies Fall 2013 Fat Tree/Clos Topology a) b) 4 ­ary 1 ­tree 4 ­ary 2 ­tree c) 4 ­ary 3 tree Interconnect Topologies Networks Communication Graph Embedding Network Properties Summary Network bus/star crossbar 1-D mesh 2-D mesh 3-D mesh n-D mesh 1-D torus 2-D torus 3-D torus n-D torus binary tree hypercube butterfly 31 Nodes k+1 k 2 + 2k k k2 k3 kn k k2 k3 kn 2k − 1 2k (k + 1)2k Deg. k 4 2 4 6 2n 2 4 6 2n 3 k 4 Diam. 2 2(k + 1) k−1 2(k − 1) 3(k − 1) n(k − 1) k/2 k 3k/2 nk/2 2(k − 1) k 2k Bisect. W. 1 k 1 k k2 k n− 1 2 2k 2k 2 2 k n− 1 1 2k − 1 2k Interconnect Topologies Michael T. Heath Parallel Numerical Algorithms Edge L. var var const const const var const const const var var var var Fall 2013 20 Things to explore    Which network suits which type of communicaBon?    Find the networks used in modern machines – Mira, Blue Waters, Stampede, Tianhe, K computer.    How does one embed one topology in another topology?    How would you connect processors? 32 Interconnect Topologies Fall 2013...
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