Computer Architecture CS 6810
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Marian Kertzmann DVM
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This 16 page Class Notes was uploaded by Marian Kertzmann DVM on Monday October 26, 2015. The Class Notes belongs to CS 6810 at University of Utah taught by Alan Davis in Fall. Since its upload, it has received 45 views. For similar materials see /class/229976/cs-6810-university-of-utah in ComputerScienence at University of Utah.
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Date Created: 10/26/15
Lecture 23 Interconnection Networks Topics communication latency centralized and decentralized switches Appendix E Topologies Internet topologies are not very regular they grew incrementally Supercomputers have regular interconnect topologies and trade off cost for high bandwidth Nodes can be connected with gt centralized switch all nodes have input and output wires going to a centralized chip that internally handles all routing gt decentralized switch each node is connected to a switch that routes data to one of a few neighbors Centralized Crossbar Switch Crossbar switch Centralized Crossbar Switch Crossbar Properties Assuming each node has one input and one output a crossbar can provide maximum bandwidth N messages can be sent as long as there are N unique sources and N unique destinations Maximum overhead WN2 internal switches where W is data width and N is number of nodes To reduce overhead use smaller switches as building blocks trade off overhead for lower effective bandwidth Switch with Omega Network 000 001 O10 011 100 101 110 111 Omega Network Properties The switch complexity is now ON log N Contention increases P0 9 P5 and P1 9 P7 cannot happen concurrently this was possible in a crossbar To deal with contention can increase the number of levels redundant paths by mirroring the network we can route from P0 to P5 via N intermediate nodes while increasing complexity by a factor of 2 Tree Network Complexity is ON Can yield low latencies when communicating with neighbors Can build a fat tree by having multiple incoming and outgoing links E E A Bisection Bandwidth Split N nodes into two groups of N2 nodes such that the bandwidth between these two groups is minimum that is the bisection bandwidth Why is it relevant if traffic is completely random the probability of a message going across the two halves is 12 if all nodes send a message the bisection bandwidth will have to be N2 The concept of bisection bandwidth confirms that the tree network is not suited for random traffic patterns but for localized traffic patterns Distributed Switches Ring Each node is connected to a 3x3 switch that routes messages between the node and its two neighbors Effectiver a repeated bus multiple messages in transit Disadvantage bisection bandwidth of 2 and N2 hops on average 39aaaaaaaa Distributed Switch Options Performance can be increased by throwing more hardware at the problem fullyconnected switches every switch is connected to every other switch N2 wiring complexity N2 4 bisection bandwidth Most commercial designs adopt a point between the two extremes ring and fullyconnected gt Grid each node connects with its N E W S neighbors gt Torus connections wrap around gt Hypercube links between nodes whose binary names differ in a single bit Topology Examples Hypercube Criteria Bus 2Dtorus 6cube Fully connected Performance Bisection bandwidth Cost Portsswitch Total links Topology Examples CH 1 Cicicp Hypercube Torus Criteria Bus Ring 2Dtorus 6cube Fully connected Performance Bisection 1 2 16 32 1024 bandwidth Cost Portsswitch 3 5 7 64 Total links 1 128 192 256 2080 13 k ary dcube Consider a kary dcube a ddimension array with k elements in each dimension there are links between elements that differ in one dimension by 1 mod k Number of nodes N kd Number Of SWitCheS 2 Avg routing distance Switch degree Diameter Number Of links 2 Bisection bandwidth PInS per node 2 Switch complexity Should we minimize or maximize dimension k ary dCube Consider a kary dcube a ddimension array with k elements in each dimension there are links between elements that differ in one dimension by 1 mod k Number of nodes N kd with no wraparound Number of switches 2 N Avg routing distance dk12 Switch degree 2d 1 Diameter 2 dk1 Number oflinks 2 Nd Bisection bandwidth 2Wkd1 Pins per node i 2wd Switch complexity 2d 12 Should we minimize or maximize dimension Title Bullet