Network Dilation: A Strategy as long as Building Families of Parallel Processing Archit

Network Dilation: A Strategy as long as Building Families of Parallel Processing Archit www.phwiki.com

Network Dilation: A Strategy as long as Building Families of Parallel Processing Archit

Kramer, George, Contributing Writer has reference to this Academic Journal, PHwiki organized this Journal Network Dilation: A Strategy as long as Building Families of Parallel Processing ArchitecturesBehrooz ParhamiDept. Electrical & Computer Eng.Univ. of Cali as long as nia, Santa BarbaraParallel Computer ArchitectureParallel computer = Nodes + Interconnects(+ Switches)B. Parhami,Plenum Press,1999Interconnection NetworksOther attributes: Regularity Scalability Packageability RobustnessNumberof nodespHeterogeneous or homogeneous nodes

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Four Example NetworksNodes p = 16Degree d = 4Diameter DBisection BLongest wireRegularityScalabilityPackageabilityRobustnessAvg. distance DSpectrum of NetworksDirect NetworksNodes (or associated routers) directly linked to each otherRouter as long as a degree-d node with q processors: d q bidirectional switch

Indirect NetworksNodes (or associated routers) linked via intermediate switchesA Sea of NetworksA Bit of History: Moving Full Circle1960sMesh-based(ILLIAC IV)Direct to indirect,shared memoryLower diameter,message passingScalability,local wiresGreaterb in addition to widthSo, only a small portion of the sea of networks has been explored in practical parallel computers 2000s

The (d, D) Graph ProblemSuppose you have an unlimited supply of degree-d nodesHow many can be connected into a network of diameter DExample 1: d = 3, D = 2; 10-node Petersen graphExample 2: d = 7, D = 2; 50-node Hoffman-Singleton graphSymmetric NetworkViewed from any node, it looks the sameImplications of Symmetry as long as NetworksA degree-4 networkRouting algorithm the same as long as every nodeNo weak spots (critical nodes or links)Maximum number of alternate paths feasibleDerivation in addition to proof of properties easierWe need to prove a particular topological or routing property as long as only one node

A Necessity as long as SymmetryUni as long as m node degree:d = 4; din = dout = 2Uni as long as m node degree is necessary but not sufficient as long as symmetryInterconnection Network ResearchTopologies as long as connecting processing nodes Devising in addition to assessing new interconnection schemesRouting algorithms in addition to their per as long as mance Oblivious / adaptive routing, deadlock avoidance/recoveryLayout in addition to packaging of networks Routing of links within / between chips, boards, cabinetsRobustness of interconnection networks Reconfiguration capabilities in addition to fault-tolerant routing Networks-on-chip (NoC) Optimal interconnection strategies as long as systems-on-chipData-center communication networks Optimized as long as data-center traffic in addition to energy efficiencyMy Personal Research HistoryWe are hereGrad 1968

The Challenge of Comparing NetworksLiszka et al.: Is an alligator better than an armadilloMy Pervious Work on Network FamiliesSystematic pruningIPL, 1998IEEE TPDS, 2001JPDC, 2005Int’l J Comp Math, 2011My Previous Work on Dilated NetworksDilation along a Hamiltonian path of a de Bruijn network(Xiao, Liang, Parhami; IPL, 2012)

Switch Networks Used in ExamplesSmall example networks to illustrate the concepts 3D hypercube = 3-cube (8 nodes, d = 3, D = 3) K4-connected cycles (12 nodes, d = 3, D = 3)3-cubeK4-connected cyclesSimplest Parallel ArchitecturesOne processing node per switch/router node D = 2 + switch network diameter d = 1 + switch network degree Degree-1 processing nodesAlternative Parallel ArchitecturesOne processing node per switch/router link D 2 switch network diameter d = switch network degree Degree-2 processing nodes

3- in addition to 2-Dilated Network Examplesk processing nodes per switch/router link D (k + 1) switch network diameter d = switch network degree Degree-2 processing nodesDiameter of Dilated NetworksThe diameter of a k-dilated network based on a diameter-Ds switch network is bounded as (k + 1)Ds D (k + 1) Ds + k Both bounds are tight, in the sense of equality being possible on both sides as long as suitably chosen networks.Worst case: All four UB UE, UB VE, VB UE, VB VE paths are diametralBest case: There is a non-diametral switch path (which can be at most one hop shorter than Ds)Proof details in my as long as thcoming Scientia Iranica paperAverage Distance in addition to Bisection WidthThe average internode distance of a k-dilated network based on a switch network with average internode hop distance Ds is D = (k + 1)Ds + k/2 + 1 + (k mod 2)/(2k).Proof details in my as long as thcoming Scientia Iranica paperThe bisection (b in addition to )width B of a dilated network remains the same as the bisection Bs of the switch network usedProof details in my as long as thcoming Scientia Iranica paper

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Aggregate B in addition to width in addition to Its ScalabilityNetwork bisection B = Bs shows lack of scalabilitySo, unless traffic is mostly local, per as long as mance will sufferAggregate b in addition to width Bagg = (k + 1)ndb [b is link b in addition to width]BW scalability ratioBSR = Bagg/D ndb/Ds BSR is sublinear in the number knd/2 of nodes For square torus of the same size: BSR = 8(knd / 2)1/2bFor hypercube of the same size: BSR = kndb / 2Connectivity in addition to RobustnessProcessing node degree of 2 precludes a connectivity > 2 Connectivity of 2 can be achieved with many switch networksAll we need is as long as 2 of the 4 paths below to be node-disjointFault diameter D + 2Wide diameter D + 2Superimposed Direct & Dilated Networksk processing nodes per some switch/router links D k + switch network diameter d = 2 switch network degree Degree-2 processing nodes

Conclusions in addition to Future WorkA strategy as long as building families of networksVariation in network size with same switch networkSame node architecture in addition to routing used throughoutApplicable to many existing or proposed networksMore network-independent / specific resultsImprove, assess, in addition to fine-tune the architecturesUse simulation to evaluate with realistic workloadsDerive scalability bounds, given per as long as mance goalsWhich networks are better as long as use with dilationFull, partial, in addition to hybrid schemes as long as network dilationQuestions or Commentsparhami@ece.ucsb.edu http://www.ece.ucsb.edu/~parhami/

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