Page - 183 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 76 Table1.Dataratecoefficientsof theclusterofDSPwith four integratedmodules (IMs). IM 1 2 3 4 1 ε α α α 2 α ε α α 3 α α ε α 4 α α α ε Thevaluesof thematrixDdependonthespecificcommunicationtopologyof the IMs. InFigure2,weconsider threeexamplesof the IMi communicationtopologyforki=4. (a) (b) (c) Figure2.ExamplesofcommunicationtopologyofDSP-processors: (a)uni-directional; (b)bi-directional; (c)all toall. Figure 2a shows uni-directional DSP communication. Let us assume that the transfer rate betweenprocessorsconnectedbyan internal linkport is equal toα= 1. Thecorrespondingmatrix ofdataratecoefficients ispresented inTable2a. Figure2bshowsbi-directionalDSPcommunication. Thecorrespondingmatrixofdataratecoefficients ispresented inTable2b. Figure2cshowsall-to-all communicationofDSP.Table2cshowsthecorrespondingdataratecoefficients. Table2.DataratecoefficientmatrixD for threecommunicationtopologiesbetweenDSP-processors. (a)Uni-Directional (b)Bi-Directional (c)All toAll 0 1 2 3 0 1 2 1 0 1 1 1 3 0 1 2 1 0 1 2 1 0 1 1 2 3 0 1 2 1 0 1 1 1 0 1 1 2 3 0 1 2 1 0 1 1 1 0 For theexperiments,wetake intoaccount twomodelsof thecluster (Figure3). In theclusterA, portsconnectonlyneighboringDSPs,asshowninFigure3a. In theclusterB,DSPsareconnectedto eachother,asshowninFigure3b. (a) (b) Figure3.DSPclusterconfiguration. (a)ClusterA; (b)ClusterB. 183