2 research outputs found
Topology Dependent Bounds For FAQs
In this paper, we prove topology dependent bounds on the number of rounds
needed to compute Functional Aggregate Queries (FAQs) studied by Abo Khamis et
al. [PODS 2016] in a synchronous distributed network under the model considered
by Chattopadhyay et al. [FOCS 2014, SODA 2017]. Unlike the recent work on
computing database queries in the Massively Parallel Computation model, in the
model of Chattopadhyay et al., nodes can communicate only via private
point-to-point channels and we are interested in bounds that work over an {\em
arbitrary} communication topology. This is the first work to consider more
practically motivated problems in this distributed model. For the sake of
exposition, we focus on two special problems in this paper: Boolean Conjunctive
Query (BCQ) and computing variable/factor marginals in Probabilistic Graphical
Models (PGMs). We obtain tight bounds on the number of rounds needed to compute
such queries as long as the underlying hypergraph of the query is
-degenerate and has -arity. In particular, the -degeneracy
condition covers most well-studied queries that are efficiently computable in
the centralized computation model like queries with constant treewidth. These
tight bounds depend on a new notion of `width' (namely internal-node-width) for
Generalized Hypertree Decompositions (GHDs) of acyclic hypergraphs, which
minimizes the number of internal nodes in a sub-class of GHDs. To the best of
our knowledge, this width has not been studied explicitly in the theoretical
database literature. Finally, we consider the problem of computing the product
of a vector with a chain of matrices and prove tight bounds on its round
complexity (over the finite field of two elements) using a novel min-entropy
based argument.Comment: A conference version was presented at PODS 201