Cell-breeding graph model for interconnection networks

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1、Cell-breedinggraphmodelforinterconnectionnetworksHaizhongShia,,YueShibaCollegeofMathematicsandStatistics,NorthwestNormalUniversity,LanzhouGansuProvince,730070,P.R.ChinabResearchCenterofBigData&GraphTech,LanzhouGansuProvince,730070,P.R.ChinaAbstractInter

2、connectionnetwork/datacenternetworkisthemostimportantpartofsupercomputer(parallelchip)/server,ofwhichtheperformancehighlyre-liesonperformanceoftheinterconnectionnetwork/datacenternetwork.Theinterconnectionnetwork/datacenternetworkcanbemodeledasagraph,inw

3、hichnoderepresentsprocessor/coreandedgerepresentscommunica-tionlink.Letr>2,Gr,whichisther-regulargraphwithnnodes,bencalledsupergraphandHr(p)(i=1;2;3),inwhichHr(p)isthegraphhasi;k1;kr(r=2p+1)nodesandcanbedecomposedintok(1kp)edgedisjointHamiltoniancycles

4、,Hr(p)isthegraphhasr(r=2p)nodesandcanbe2;kdecomposedintok(1kp1)edgedisjointHamiltoniancyclesandaperfectmatchingandHr(p)isthegraphhasr(r=2p)nodesandcanbe3;kdecomposedintok(1kp1)edgedisjointHamiltoncycles,becalledcellgraphs.Inthispaper,weconstructagr

5、aphGrHr(p)byreplacingeveryni;knodeofGrwithHr(p)andnameitasi-type1-timescell-breedinggraphni;kfromthesplittingandbreedingofsupergraphGrandcellgraphHr(p)(i=ni;k1;2;3);furthermore,wecanconstructthei-type2-timescell-breedinggraph,i-type3-timescell-breedinggr

6、aph,...,i-type(m+1)timescell-breedinggraph.Particularly,whenGriscompletegraph,Cayleygraph(e.g,Starngraph,Bubblesortgraph,etc)orHypercubegraphanditsvariations(e.g,undirectedtoroidalmesh,crossedcubes,foldedcubes,etc),weobtainmanykindsofinterconnectionnetw

7、orks,whicharedifferentcharacteristics.Keywords:Supercomputer,Interconnectionnetwork,Regulargraph,SuperCorrespondingauthorEmailaddresses:haizhong.shi@163.com(HaizhongShi),GraphTech.Yue@outlook.com(YueShi)PreprintsubmittedtoDiscreteAppliedMathematicsJanuar

8、y9,2015graph,Cellgraph,Cell-breedinggraph1.IntroductionWiththeconsistentupdateofsupercomputer,theupgradeofserverswithinbigdatacenterandtheparallelizationofchips,thedevelopmentofnewinterconnectionnetworkswithbetterperforman