Evaluating Datalog over Semirings: A Grounding-based Approach
arxiv(2024)
摘要
Datalog is a powerful yet elegant language that allows expressing recursive
computation. Although Datalog evaluation has been extensively studied in the
literature, so far, only loose upper bounds are known on how fast a Datalog
program can be evaluated. In this work, we ask the following question: given a
Datalog program over a naturally-ordered semiring σ, what is the
tightest possible runtime? To this end, our main contribution is a general
two-phase framework for analyzing the data complexity of Datalog over σ:
first ground the program into an equivalent system of polynomial equations
(i.e. grounding) and then find the least fixpoint of the grounding over
σ. We present algorithms that use structure-aware query evaluation
techniques to obtain the smallest possible groundings. Next, efficient
algorithms for fixpoint evaluation are introduced over two classes of
semirings: (1) finite-rank semirings and (2) absorptive semirings of total
order. Combining both phases, we obtain state-of-the-art and new algorithmic
results. Finally, we complement our results with a matching fine-grained lower
bound.
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