Semidefinite optimization of High Performance Linpack on heterogeneous cluster

High Performance Linpack (HPL) is an industry standard benchmark used in measuring the computational power of High Performance Clusters. In contrary to HPC clusters consisting of equal computational nodes, running HPL on heterogeneous HPC clusters, built up of a computing nodes with different computational power, showed in most cases poor efficiency. In such type of clusters, efficiency of HPL further decreases if the speed of interconnect links between computing nodes is different. In order to improve HPL efficiency on such a clusters, one needs to optimally balance HPL workload on computing nodes accordingly to their computational power, and at the same time, take into the consideration the speed of communication links between them. Our thesis is that the problem of efficiently running HPL on heterogeneous HPC cluster is solvable, and that one can formulate it as a Semidefinite Optimization of Second Eigenvalue in Magnitude (SLEM) matrix describing data-flow of HPL in a cluster. In order to test a validity of such an approach, we run a series of HPL benchmarks on Isabella HPC cluster, both optimized respective to SLEM and non-optimized. By comparing results obtained with SLEM optimization of HPL against non-optimized HPL, we were able to identify a huge improvement in HPL efficiency when using SLEM. Moreover, by taking into the consideration memory sizes of computational nodes, we were able to improve SLEM optimization of HPL further.