Optimal remapping in dynamic bulk synchronous computations via a stochastic control approach

A bulk synchronous computation proceeds in phases that are separated by barrier synchronization. For dynamic bulk synchronous computations that exhibit varying phase-wise computational requirements, remapping at runtime is an effective approach to ensure parallel efficiency. The paper introduces a novel remapping strategy for computations whose workload changes can be modeled as a Markov chain. The use of a Markovian model allows us to treat statistical dependence and more complex structure than the usual independent identically distributed random variable assumptions. Our models are quite general and we do not need to impose conditions on the dynamics of the underlying process other than the transition probability matrix. It is shown that optimal remapping can be formulated as a binary decision process: remap or not at a given synchronizing instant. The optimal strategy is then developed for long lasting computations by employing optimal stopping rules in a stochastic control framework. The existence of optimal controls is established. Necessary and sufficient conditions for the optimality are obtained. Furthermore, a policy iteration algorithm is devised to reduce computational complexity and enhance fast convergence to the desired optimal control.