On the CALM Principle for BSP Computation

In recent times, considerable emphasis has been given to two apparently disjoint research topics: data-parallel and eventually consistent, distributed systems. In this paper we propose a study on an eventually consistent, dataparallel computational model, the keystone of which is provided by the recent finding that a class of programs exists that can be computed in an eventually consistent, coordination-free way: monotonic programs. This principle is called CALM and has been proven by Ameloot et al. for distributed, asynchronous settings. We advocate that CALM should be employed as a basic theoretical tool also for data-parallel systems, wherein computation usually proceeds synchronously in rounds and where communication is assumed to be reliable. We deem this problem relevant and interesting, especially for what concerns parallel workflow optimization, and make the case that CALM does not hold in general for dataparallel systems if the techniques developed by Ameloot et al. are directly used. In this paper we sketch how, using novel techniques, the satisfiability of the if direction of the CALM principle can still be obtained, although just for a subclass of monotonic queries.