On stalling in LogP

We investigate the issue of stalling in the LogP model. In particular, we introduce a novel quantitative characterization of stalling, referred to as δ-stalling, which intuitively captures the realistic assumption that once the network's capacity constraint is violated, it takes some time (at most δ) for this information to propagate to the processors involved. We prove a lower bound that shows that LogP under δ-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 δ-stalling LogP with δ=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 Bilardi et al. (Algorithmica 24 (1999) 405) and Ramachandran et al. (J. Parallel Distributed Comput. 63 (2003) 1175) to the more powerful L-stalling LogP.