E-differentiation for analyzing scalability of parallel algorithms on parallel architectures

The E-differentiation, which is derived from the idea of isoefficiency analysis and used for analyzing scalability of parallel algorithms on parallel architectures, is proposed in this paper. The basic philosophy of E-differentiation is that scalability analysis should be based on the ratio of the change of E (efficiency of processors) vs. W (Workload), E_w^´, and E vs. P (number of processors), E_p´. E-differentiation can overcome the incompletion of other metrics for analyzing scalability with assumptions which confine the manner of the increasement of W w.r.t. p; and it is easy to give the equivalent expression of these metrics in terms of E-differentiation so that relationships between these metrics can be studied more definitively. Because E-differentiation does not the restrict of isoefficiency, which confines the generality of the isoefficiency analysis, it can measure the scalability of any parallel algorithms on any parallel architectures, and can predict the change of performance of parallel algorithms when change manner of W w.r.t. p does not follow isoefficiency function