39,868 research outputs found
Solving equations in the relational algebra
Enumerating all solutions of a relational algebra equation is a natural and
powerful operation which, when added as a query language primitive to the
nested relational algebra, yields a query language for nested relational
databases, equivalent to the well-known powerset algebra. We study
\emph{sparse} equations, which are equations with at most polynomially many
solutions. We look at their complexity, and compare their expressive power with
that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin
Some relational structures with polynomial growth and their associated algebras II: Finite generation
The profile of a relational structure is the function which
counts for every integer the number, possibly infinite, of
substructures of induced on the -element subsets, isomorphic
substructures being identified. If takes only finite values, this
is the Hilbert function of a graded algebra associated with , the age
algebra , introduced by P.~J.~Cameron.
In a previous paper, we studied the relationship between the properties of a
relational structure and those of their algebra, particularly when the
relational structure admits a finite monomorphic decomposition. This
setting still encompasses well-studied graded commutative algebras like
invariant rings of finite permutation groups, or the rings of quasi-symmetric
polynomials.
In this paper, we investigate how far the well know algebraic properties of
those rings extend to age algebras. The main result is a combinatorial
characterization of when the age algebra is finitely generated. In the special
case of tournaments, we show that the age algebra is finitely generated if and
only if the profile is bounded. We explore the Cohen-Macaulay property in the
special case of invariants of permutation groupoids. Finally, we exhibit
sufficient conditions on the relational structure that make naturally the age
algebra into a Hopf algebra.Comment: 27 pages; submitte
Inference Optimization using Relational Algebra
Exact inference procedures in Bayesian networks can be expressed using relational algebra; this provides a common ground for optimizations from the AI and database communities. Specifically, the ability to accomodate sparse representations of probability distributions opens up the way to optimize for their cardinality instead of the dimensionality; we apply this in a sensor data model.\u
Analysing Temporal Relations – Beyond Windows, Frames and Predicates
This article proposes an approach to rely on the standard
operators of relational algebra (including grouping and ag-
gregation) for processing complex event without requiring
window specifications. In this way the approach can pro-
cess complex event queries of the kind encountered in appli-
cations such as emergency management in metro networks.
This article presents Temporal Stream Algebra (TSA) which
combines the operators of relational algebra with an analy-
sis of temporal relations at compile time. This analysis de-
termines which relational algebra queries can be evaluated
against data streams, i. e. the analysis is able to distinguish
valid from invalid stream queries. Furthermore the analysis
derives functions similar to the pass, propagation and keep
invariants in Tucker's et al. \Exploiting Punctuation Seman-
tics in Continuous Data Streams". These functions enable
the incremental evaluation of TSA queries, the propagation
of punctuations, and garbage collection. The evaluation of
TSA queries combines bulk-wise and out-of-order processing
which makes it tolerant to workload bursts as they typically
occur in emergency management. The approach has been
conceived for efficiently processing complex event queries on
top of a relational database system. It has been deployed
and tested on MonetDB
An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications
Alloy is a lightweight modeling formalism based on relational algebra. In
prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have
presented a tool, Alchemy, that compiles Alloy specifications into
implementations that execute against persistent databases. The foundation of
Alchemy is an algorithm for rewriting relational algebra formulas into code for
database transactions. In this paper we report on recent progress in improving
the robustness and efficiency of this transformation
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