A new model for interconnection network k-hierarchical ring and r-layer graph network

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1、July8,201516:42WSPC/INSTRUCTIONFILEws-joinJournalofInterconnectionNetworks⃝cWorldScientificPublishingCompanyAnewmodelforinterconnectionnetwork:k-hierarchicalringandr-layergraphnetworkHaizhongShiCollegeofMathematicsandStatistics,NorthwestNormalUniversity,LanzhouGansuProvince,730070,P.R.Chinay

2、haizhong.shi@163.comzYueShiResearchCenterofBigData&GraphTech,LanzhouGansuProvince,730070,P.R.ChinaGraphTech.Yue@outlook.comReceivedDayMonthYearRevisedDayMonthYearInterconnectionnetwork/on-chipinterconnectionnetwork/datacenternetworkisthemostimportantpartofsupercomputer/parallelchip/datacente

3、rserver,ofwhichtheperfor-mancehighlyreliesonperformanceoftheinterconnectionnetwork/on-chipinterconnec-tionnetwork/datacenternetwork.Theinterconnectionnetwork/on-chipinterconnectionnetwork/datacenternetworkcanbemodeledasagraph,inwhicheachnoderepresentsaprocessor/core/serverandeachedgerepresen

4、tsacommunicationlink.N-dimensionaltorusnetworks,whichwasemployedby”KingSupercomputer”and”SequoiaSupercomputer”,hasbeenoneofthemostfamousinterconnectionnetworks.Alongwithn-dimensionaltorusnetwork,ringnetwork,hypercubeandstarnetworketcarealsotypicalinterconnec-tionnetworks,buttheyareallofbotha

5、dvantagesanddisadvantages.Inthispaper,weproposeanewmodelforinterconnectionnetwork—k-hierarchicalringandr-layergraphnetwork:ononehand,weprovethatn-dimensionaltorusnetwork,ringnetwork,hyper-cubeandstarnetworketcareallspecialk-hierarchicalringandr-layergraphnetworks;ontheotherhand,weemploythism

6、odeltodesigncertaininterconnectionnetworksincluding1-hierarchicalringand2-layerstarnetwork,1-hierarchicalringand2-layercube-starnet-work,1-hierarchicalringand1-layerstar-connected-cyclesnetwork,1-hierarchicalringand2-layerstar-connected-cyclesnetworkand2-hierarchicalringand1-layerstar-connec

7、ted-cyclenetwork.Inparticular,whenincomparablesizes,thedegrees(d=9;10;11)of1-hierarchicalringand2-layerstarnetworkZl×Sq×Sn(q=4;n=5;6;7)arealllargerthanthedegree(d=6)of3-dimensionaltorusnetwork,butthediametersofthesethreenetworksareonlynearlyone-ten