The standard Linpack benchmark employed for the Top500 list solves a

2. The standard Linpack benchmark employed for the Top500 list solves a dense mxm system of linear equations. The time complexity for the sequential algorithm can be approximated by 2/3m3+2m2 Assuming there is a MPI parallel Linpack code which requires: T(n) = 2km +? mWhere k is a hardware-dependant constant. Answer the following questions assuming the parallel code has no sequential bottleneck, and executed on a 10,000-node cluster. [30 marks] a) Using the canonical Amdahl's law, calculate the value of k where the cluster can deliver an efficiency of 99% speedup using the parallel code for Linpack 100 and Linpack 1000 (i.e. matrices of order 100 and 1000 respectively). [15 marks] b) Assume now a MPI implementation which incorporates the MP-3 RMA interface and has a k=1. i What is the new speedun and efficiency for Linpack 100 and 1000? 2. The standard Linpack benchmark employed for the Top500 list solves a dense mxm system of linear equations. The time complexity for the sequential algorithm can be approximated by 2/3m3+2m2 Assuming there is a MPI parallel Linpack code which requires: T(n) = 2km +? mWhere k is a hardware-dependant constant. Answer the following questions assuming the parallel code has no sequential bottleneck, and executed on a 10,000-node cluster. [30 marks] a) Using the canonical Amdahl's law, calculate the value of k where the cluster can deliver an efficiency of 99% speedup using the parallel code for Linpack 100 and Linpack 1000 (i.e. matrices of order 100 and 1000 respectively). [15 marks] b) Assume now a MPI implementation which incorporates the MP-3 RMA interface and has a k=1. i What is the new speedun and efficiency for Linpack 100 and 1000