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A large class of traditional graph and data mining algorithms can beconcisely expressed in Datalog, and other Logic-based languages, onceaggregates are allowed in recursion. In fact, for most BigData algorithms, thedifficult semantic issues raised by the use of non-monotonic aggregates inrecursion are solved by Pre-Mappability (PreM), a property that assures thatfor a program with aggregates in recursion there is an equivalentaggregate-stratified program. In this paper we show that, by bringing togetherthe formal abstract semantics of stratified programs with the efficientoperational one of unstratified programs, PreM can also facilitate and improvetheir parallel execution. We prove that PreM-optimized lock-free anddecomposable parallel semi-naive evaluations produce the same results as thesingle executor programs. Therefore, PreM can be assimilated into thedata-parallel computation plans of different distributed systems, irrespectiveof whether these follow bulk synchronous parallel (BSP) or asynchronouscomputing models. In addition, we show that non-linear recursive queries can beevaluated using a hybrid stale synchronous parallel (SSP) model on distributedenvironments. After providing a formal correctness proof for the recursivequery evaluation with PreM under this relaxed synchronization model, we presentexperimental evidence of its benefits. This paper is under consideration foracceptance in Theory and Practice of Logic Programming (TPLP).

A Case for Stale Synchronous Distributed Model for Declarative Recursive Computation