Evaluating the Power of the Parallel Masc Model Using Simulations and Real-time Applications

ion for algorithm design and programming, while LogP provides better control of machine resources. Comparisons and evaluations between the two models have been made in [29,62,104]. In [29], a variant of LogP that disallows the so-called stalling behavior is considered. The authors create cross simulations between the two models showing their equivalence in algorithmic design when using asymptotic analysis. A non-stalling LogP(L, o, G, P) algorithm can be simulated on BSP(l, g) with slowdown O(1+g / G + l / L). When l = Θ(L) and g = Θ(G), the slowdown is constant. On the other hand, a BSP 39 superstep involving at most w local operations per processors and the routing of an hrelation can be simulated in non-stalling LogP with worst-case time O(w + (Gh + L)S(L, G, p, h)). Here S(L, G, p, h) is a function of L, G, p, h with the value of O(1) when h = Ω(pε +L log p) and O(log p) otherwise. This indicates that, when the bandwidth and latency parameters have the same value in both models, BSP can simulate LogP with constant slowdown and LogP can simulate BSP with at most logarithmic slowdown. Hence, within the asymptotic limits, BSP and non-stalling LogP can be viewed as closely related variants within the bandwidth-latency framework for modeling parallel computation. BSP seems somewhat preferable due to its greater simplicity and portability, and slightly greater power. Recently, the authors of [104] improve the above results to the stalling LogP model. A non-stalling LogG algorithm can be simulated deterministically efficiently on BSP with slowdown l/L. However, for a stalling LogP, any deterministic step-by-step simulation of LogP on BSP can have arbitrary large slowdown and there is no deterministic step-by-step simulation of stalling LogP on BSP that is efficient. It has also been shown that the two models can be implemented with similar performance on most point-to-point network [29,35,62,123]. BSP could outweigh the advantages by more convenient programming abstraction and better software portability. On the other hand, BSP assumes special hardware support to synchronize all processors at the end of superstep. This may not be available on many parallel machines, especially in the generality where not multiple arbitrary subsets of the processors can synchronize.