3,915 research outputs found
A survey of parallel execution strategies for transitive closure and logic programs
An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods
The Markov chain tree theorem and the state reduction algorithm in commutative semirings
We extend the Markov chain tree theorem to general commutative semirings, and
we generalize the state reduction algorithm to commutative semifields. This
leads to a new universal algorithm, whose prototype is the state reduction
algorithm which computes the Markov chain tree vector of a stochastic matrix.Comment: 13 page
Optimal Topology Design for Disturbance Minimization in Power Grids
The transient response of power grids to external disturbances influences
their stable operation. This paper studies the effect of topology in linear
time-invariant dynamics of different power grids. For a variety of objective
functions, a unified framework based on norm is presented to analyze the
robustness to ambient fluctuations. Such objectives include loss reduction,
weighted consensus of phase angle deviations, oscillations in nodal frequency,
and other graphical metrics. The framework is then used to study the problem of
optimal topology design for robust control goals of different grids. For radial
grids, the problem is shown as equivalent to the hard "optimum communication
spanning tree" problem in graph theory and a combinatorial topology
construction is presented with bounded approximation gap. Extended to loopy
(meshed) grids, a greedy topology design algorithm is discussed. The
performance of the topology design algorithms under multiple control objectives
are presented on both loopy and radial test grids. Overall, this paper analyzes
topology design algorithms on a broad class of control problems in power grid
by exploring their combinatorial and graphical properties.Comment: 6 pages, 3 figures, a version of this work will appear in ACC 201
From Sequential Layers to Distributed Processes, Deriving a minimum weight spanning tree algorithm
Analysis and design of distributed algorithms and protocols are difficult issues. An important cause for those difficulties is the fact that the logical structure of the solution is often invisible in the actual implementation. We introduce a framework that allows for a formal treatment of the design process, from an abstract initial design to an implementation tailored to specific architectures. A combination of algebraic and axiomatic techniques is used to verify correctness of the derivation steps. This is shown by deriving an implementation of a distributed minimum weight spanning tree algorithm in the style of [GHS]
Vacancy localization in the square dimer model
We study the classical dimer model on a square lattice with a single vacancy
by developing a graph-theoretic classification of the set of all configurations
which extends the spanning tree formulation of close-packed dimers. With this
formalism, we can address the question of the possible motion of the vacancy
induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy
to be strictly jammed in an infinite system. More generally, the size
distribution of the domain accessible to the vacancy is characterized by a
power law decay with exponent 9/8. On a finite system, the probability that a
vacancy in the bulk can reach the boundary falls off as a power law of the
system size with exponent 1/4. The resultant weak localization of vacancies
still allows for unbounded diffusion, characterized by a diffusion exponent
that we relate to that of diffusion on spanning trees. We also implement
numerical simulations of the model with both free and periodic boundary
conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure
9), a shift s->s+1 in the definition of the tree size, and minor correction
Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of
tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary
number of gluons and gravitons, which is valid for general spacetime dimensions
and any helicity configurations. The recursion is written in terms of
fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be
further carried out until we reach an expansion in terms of pure YM amplitudes
in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning
tree structure rooted on gluons whose vertices are gravitons. We further
propose a set of graph theoretical rules based on spanning trees that evaluate
directly the pure YM expansion coefficients.Comment: 36 pages, 3 captioned figures; v2: more details added, revised and
published versio
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