110,670 research outputs found
Nested Regular Path Queries in Description Logics
Two-way regular path queries (2RPQs) have received increased attention
recently due to their ability to relate pairs of objects by flexibly navigating
graph-structured data. They are present in property paths in SPARQL 1.1, the
new standard RDF query language, and in the XML query language XPath. In line
with XPath, we consider the extension of 2RPQs with nesting, which allows one
to require that objects along a path satisfy complex conditions, in turn
expressed through (nested) 2RPQs. We study the computational complexity of
answering nested 2RPQs and conjunctions thereof (CN2RPQs) in the presence of
domain knowledge expressed in description logics (DLs). We establish tight
complexity bounds in data and combined complexity for a variety of DLs, ranging
from lightweight DLs (DL-Lite, EL) up to highly expressive ones. Interestingly,
we are able to show that adding nesting to (C)2RPQs does not affect worst-case
data complexity of query answering for any of the considered DLs. However, in
the case of lightweight DLs, adding nesting to 2RPQs leads to a surprising jump
in combined complexity, from P-complete to Exp-complete.Comment: added Figure
Thou Shalt Covet The Average Of Thy Neighbors' Cakes
We prove an lower bound on the query complexity of local
proportionality in the Robertson-Webb cake-cutting model. Local proportionality
requires that each agent prefer their allocation to the average of their
neighbors' allocations in some undirected social network. It is a weaker
fairness notion than envy-freeness, which also has query complexity
, and generally incomparable to proportionality, which has query
complexity . This result separates the complexity of local
proportionality from that of ordinary proportionality, confirming the intuition
that finding a locally proportional allocation is a more difficult
computational problem
An Algorithmic Argument for Nonadaptive Query Complexity Lower Bounds on Advised Quantum Computation
This paper employs a powerful argument, called an algorithmic argument, to
prove lower bounds of the quantum query complexity of a multiple-block ordered
search problem in which, given a block number i, we are to find a location of a
target keyword in an ordered list of the i-th block. Apart from much studied
polynomial and adversary methods for quantum query complexity lower bounds, our
argument shows that the multiple-block ordered search needs a large number of
nonadaptive oracle queries on a black-box model of quantum computation that is
also supplemented with advice. Our argument is also applied to the notions of
computational complexity theory: quantum truth-table reducibility and quantum
truth-table autoreducibility.Comment: 16 pages. An extended abstract will appear in the Proceedings of the
29th International Symposium on Mathematical Foundations of Computer Science,
Lecture Notes in Computer Science, Springer-Verlag, Prague, August 22-27,
200
Query-Efficient Locally Decodable Codes of Subexponential Length
We develop the algebraic theory behind the constructions of Yekhanin (2008)
and Efremenko (2009), in an attempt to understand the ``algebraic niceness''
phenomenon in . We show that every integer ,
where , and are prime, possesses the same good algebraic property as
that allows savings in query complexity. We identify 50 numbers of this
form by computer search, which together with 511, are then applied to gain
improvements on query complexity via Itoh and Suzuki's composition method. More
precisely, we construct a -query LDC for every positive
integer and a -query
LDC for every integer , both of length , improving the
queries used by Efremenko (2009) and queries used by Itoh and
Suzuki (2010).
We also obtain new efficient private information retrieval (PIR) schemes from
the new query-efficient LDCs.Comment: to appear in Computational Complexit
Computing Possible and Certain Answers over Order-Incomplete Data
This paper studies the complexity of query evaluation for databases whose
relations are partially ordered; the problem commonly arises when combining or
transforming ordered data from multiple sources. We focus on queries in a
useful fragment of SQL, namely positive relational algebra with aggregates,
whose bag semantics we extend to the partially ordered setting. Our semantics
leads to the study of two main computational problems: the possibility and
certainty of query answers. We show that these problems are respectively
NP-complete and coNP-complete, but identify tractable cases depending on the
query operators or input partial orders. We further introduce a duplicate
elimination operator and study its effect on the complexity results.Comment: 55 pages, 56 references. Extended journal version of
arXiv:1707.07222. Up to the stylesheet, page/environment numbering, and
possible minor publisher-induced changes, this is the exact content of the
journal paper that will appear in Theoretical Computer Scienc
Tree-like Queries in OWL 2 QL: Succinctness and Complexity Results
This paper investigates the impact of query topology on the difficulty of
answering conjunctive queries in the presence of OWL 2 QL ontologies. Our first
contribution is to clarify the worst-case size of positive existential (PE),
non-recursive Datalog (NDL), and first-order (FO) rewritings for various
classes of tree-like conjunctive queries, ranging from linear queries to
bounded treewidth queries. Perhaps our most surprising result is a
superpolynomial lower bound on the size of PE-rewritings that holds already for
linear queries and ontologies of depth 2. More positively, we show that
polynomial-size NDL-rewritings always exist for tree-shaped queries with a
bounded number of leaves (and arbitrary ontologies), and for bounded treewidth
queries paired with bounded depth ontologies. For FO-rewritings, we equate the
existence of polysize rewritings with well-known problems in Boolean circuit
complexity. As our second contribution, we analyze the computational complexity
of query answering and establish tractability results (either NL- or
LOGCFL-completeness) for a range of query-ontology pairs. Combining our new
results with those from the literature yields a complete picture of the
succinctness and complexity landscapes for the considered classes of queries
and ontologies.Comment: This is an extended version of a paper accepted at LICS'15. It
contains both succinctness and complexity results and adopts FOL notation.
The appendix contains proofs that had to be omitted from the conference
version for lack of space. The previous arxiv version (a long version of our
DL'14 workshop paper) only contained the succinctness results and used
description logic notatio
Expressivity and Complexity of MongoDB Queries
In this paper, we consider MongoDB, a widely adopted but not formally understood database system managing JSON documents and equipped with a powerful query mechanism, called the aggregation framework. We provide a clean formal abstraction of this query language, which we call MQuery. We study the expressivity of MQuery, showing the equivalence of its well-typed fragment with nested relational algebra. We further investigate the computational complexity of significant fragments of it, obtaining several (tight) bounds in combined complexity, which range from LogSpace to alternating exponential-time with a polynomial number of alternations
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