On stalling in LogP ? ( Extended

We investigate the issue of stalling in the LogP model. In particular, we introduce a novel quantitative characterization of stalling, referred to as -stalling, which intuitively captures the realistic assumption that once the network’s capacity constraint is violated, it takes some time (at most ) for this information to propagate to the processors involved. We prove a lower bound that shows that LogP under -stalling is strictly more powerful than the stall-free version of the model where only strictly stall-free computations are permitted. On the other hand, we show that -stalling LogP with = L can be simulated with at most logarithmic slowdown by a BSP machine with similar bandwidth and latency values, thus extending the equivalence (up to logarithmic factors) between stall-free LogP and BSP argued in [1] to the more powerful L-stalling LogP.