Is the MapReduce framework a type of BSP? Is it accurate to call the mapReduce framework a type of bulk synchronous parallel programming framework with no local memory retention within processors between synchronizations? If not, what parallel programming model most accurately encapsulates the mapReduce framework?
In section 2 of http://arxiv.org/abs/1101.1902, the authors define a model of MapReduce that is intentionally structured like BSP. They prove simulation theorems as well. May be a good place to start.