Jaguar：一种用于子模宽度时间内联合查询评估的原始算法
Jaguar: A Primal Algorithm for Conjunctive Query Evaluation in Submodular-Width Time
AI总结：
本文提出一种新的联合查询评估算法Jaguar，其在子模宽度时间内实现高效查询处理，且算法描述和分析比PANDA更简洁。
摘要：
子模宽度是联合查询（CQ）的一种复杂度度量，为每个CQ Q分配一个非负实数，子模宽度（Q）。现有算法PAND在多项式时间内执行CQ评估，指数本质上为subw(Q)。形式上，对于每个布尔CQ Q，PANDA在时间O(N^{subw(Q)} · polylog(N))内评估Q；此外，有复杂性理论证据表明，对于某些布尔CQ，无法通过组合算法获得严格低于subw(Q)的指数。子模宽度可以描述为所有多项式族的最大值，这些多项式族是Q变量上的集合函数，满足香农不等式。PANDA算法在某种程度上在该最大化问题的对偶空间中工作，利用信息论，并将CQ转换为一组析取性Datalog程序，这些程序分别解决。本文介绍了一种新的CQ评估算法，对于每个布尔CQ Q和所有ε>0，运行时间为O(N^{subw(Q)+ε})。我们认为该算法的描述和分析比PANDA显著更简洁。我们称之为“原始”算法，因为它在描述的最大化问题的原始空间中工作，通过维护一个可行的原始解，即多项式族。确实，该算法直接处理输入CQ，并自适应计算一系列连接，以指导的方式，使得这些连接计算的成本被限制。此外，该算法可以实现对于包含度约束的子模宽度扩展的运行时间。我们称该算法为Jaguar，因为它是一种连接自适应的引导算法。
英文摘要：
The submodular width is a complexity measure of conjunctive queries (CQs), which assigns a nonnegative real number, subw(Q), to each CQ Q. An existing algorithm, called PAND, performs CQ evaluation in polynomial time where the exponent is essentially subw(Q). Formally, for every Boolean CQ Q, PANDA evaluates Q in time $O(N^{\mathsf{subw}(Q)} \cdot \mathsf{polylog}(N))$, where N denotes the input size; moreover, there is complexity-theoretic evidence that, for a number of Boolean CQs, no exponent strictly below subw(Q) can be achieved by combinatorial algorithms. On a high level, the submodular width of a CQ Q can be described as the maximum over all polymatroids, which are set functions on the variables of Q that satisfy Shannon inequalities. The PANDA algorithm in a sense works in the dual space of this maximization problem, makes use of information theory, and transforms a CQ into a set of disjunctive datalog programs which are individually solved. In this article, we introduce a new algorithm for CQ evaluation which achieves, for each Boolean CQ Q and for all epsilon > 0, a running time of $O(N^{\mathsf{subw}(Q)+ε})$. This new algorithm's description and analysis are, in our view, significantly simpler than those of PANDA. We refer to it as a "primal" algorithm as it operates in the primal space of the described maximization problem, by maintaining a feasible primal solution, namely, a polymatroid. Indeed, this algorithm deals directly with the input CQ and adaptively computes a sequence of joins, in a guided fashion, so that the cost of these join computations is bounded. Additionally, this algorithm can achieve the stated runtime for the generalization of the submodular width incorporating degree constraints. We dub our algorithm Jaguar, as it is a join-adaptive guided algorithm.
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