Tractable Orders for Direct Access to Ranked Answers of Conjunctive Queries
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by
Nofar Carmeli, Nikolaos Tziavelis, Wolfgang Gatterbauer, Benny Kimelfeld, Mirek Riedewald
2020
Abstract
We study the question of when we can answer a Conjunctive Query (CQ) with an
ordering over the answers by constructing a structure for direct (random)
access to the sorted list of answers, without actually materializing this list,
so that the construction time is linear (or quasilinear) in the size of the
database. In the absence of answer ordering, such a construction has been
devised for the task of enumerating query answers of free-connex acyclic CQs,
so that the access time is logarithmic. Moreover, it follows from past results
that within the class of CQs without self-joins, being free-connex acyclic is
necessary for the existence of such a construction (under conventional
assumptions in fine-grained complexity).
In this work, we embark on the challenge of identifying the answer orderings
that allow for ranked direct access with the above complexity guarantees. We
begin with the class of lexicographic orderings and give a decidable
characterization of the class of feasible such orderings for every CQ without
self-joins. We then continue to the more general case of orderings by the sum
of attribute scores. As it turns out, in this case ranked direct access is
feasible only in trivial cases. Hence, to better understand the computational
challenge at hand, we consider the more modest task of providing access to only
one single answer (i.e., finding the answer at a given position). We indeed
achieve a quasilinear-time algorithm for a subset of the class of full CQs
without self-joins, by adopting a solution of Frederickson and Johnson to the
classic problem of selection over sorted matrices. We further prove that none
of the other queries in this class admit such an algorithm.
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