Jaguar: A Primal Algorithm for Conjunctive Query Evaluation in Submodular-Width Time
Mahmoud Abo Khamis, Hubie Chen

TL;DR
Jaguar is a new, simpler primal algorithm for evaluating conjunctive queries efficiently in submodular-width time, improving upon prior dual-space methods with adaptive join strategies.
Contribution
Introduces Jaguar, a primal algorithm that achieves near-optimal submodular-width time bounds with a more straightforward approach than existing methods.
Findings
Jaguar operates in $O(N^{subw(Q)+psilon})$ time for all psilon > 0.
Jaguar's design is simpler than the PANDA algorithm, focusing on primal space.
The algorithm extends to handle degree constraints in query evaluation.
Abstract
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 , 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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
