scholarly journals Quasipolynomial Set-Based Symbolic Algorithms for Parity Games

10.29007/5z5k ◽  
2018 ◽  
Author(s):  
Krishnendu Chatterjee ◽  
Wolfgang Dvořák ◽  
Monika Henzinger ◽  
Alexander Svozil
Keyword(s):  
Explicit Representation ◽  
Algorithmic Problem ◽  
Scalable Algorithms ◽  
Basic Algorithm ◽  
Important Special Case ◽  
Symbolic Space ◽  
Basic Set ◽  
Parity Games ◽  
Symbolic Algorithm ◽  
Symbolic Algorithms

Solving parity games, which are equivalent to modal μ-calculus model checking, is a central algorithmic problem in formal methods, with applications in reactive synthesis, program repair, verification of branching-time properties, etc. Besides the standard compu- tation model with the explicit representation of games, another important theoretical model of computation is that of set-based symbolic algorithms. Set-based symbolic algorithms use basic set operations and one-step predecessor operations on the implicit description of games, rather than the explicit representation. The significance of symbolic algorithms is that they provide scalable algorithms for large finite-state systems, as well as for infinite-state systems with finite quotient. Consider parity games on graphs with n vertices and parity conditions with d priorities. While there is a rich literature of explicit algorithms for parity games, the main results for set-based symbolic algorithms are as follows: (a) the basic algorithm that requires O(nd) symbolic operations and O(d) symbolic space; and (b) an improved algorithm that requires O(nd/3+1) symbolic operations and O(n) symbolic space. In this work, our contributions are as follows: (1) We present a black-box set-based symbolic algorithm based on the explicit progress measure algorithm. Two important consequences of our algorithm are as follows: (a) a set-based symbolic algorithm for parity games that requires quasi-polynomially many symbolic operations and O(n) symbolic space; and (b) any future improvement in progress measure based explicit algorithms immediately imply an efficiency improvement in our set-based symbolic algorithm for parity games. (2) We present a set-based symbolic algorithm that requires quasi-polynomially many symbolic operations and O(d · log n) symbolic space. Moreover, for the important special case of d ≤ log n, our algorithm requires only polynomially many symbolic operations and poly-logarithmic symbolic space.

scholarly journals Strengthening ties towards a highly-connected world

2022 ◽  
Author(s):  
Antonis Matakos ◽  
Aristides Gionis
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Constant Factor ◽  
Algorithmic Problem ◽  
Full Potential ◽  
User Engagement ◽  
Scalable Algorithms ◽  
Special Cases ◽  
Access Information ◽  
Flow Of Information

AbstractOnline social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms.

USE OF GENERALIZED SCHEMES IN TEACHING PROGRAMMING

2019 ◽  
pp. 37-40
Author(s):  
N. Yu. Dobrovolskaia
Keyword(s):  
Problem Solving ◽  
Algorithmic Problem ◽  
Basic Algorithm ◽  
Modular Programming ◽  
Training Materials ◽  
Programming Skills

The article discusses the use of generalized schemes as language independent fragments of algorithmic problem solving in the design of training materials, the generation of sets of multilevel test tasks. The use of schemes in teaching programming develops in schoolchildren the ability to formalize a problem, to correlate its solution with the basic algorithm, and to establish block-modular programming skills.

The effects and use of negative pressure wound therapy – a set of case reports

2020 ◽  
Vol 99 (4) ◽  
pp. 183-188
Keyword(s):  
Wound Healing ◽  
High Risk ◽  
Negative Pressure ◽  
Negative Pressure Wound Therapy ◽  
Chronic Wounds ◽  
Wide Spectrum ◽  
Case Reports ◽  
Modern Medicine ◽  
Wound Therapy ◽  
Basic Set

Modern medicine offers a wide spectrum of wound healing resources for acute or chronic wounds. Negative pressure wound therapy (NPWT) is a very effective method, allowing complicated defects and wounds to heal. The basic set is usually provided with various special accessories to facilitate the use and support safe application of NPWT to high-risk tissue. Selected case reports are presented herein to document the special use and combinations of materials in negative pressure wound therapy.

An Alternate Algorithm for (3x3) Median Filtering of Digital Images

2012 ◽  
Vol 2 (1) ◽  
pp. 7-9 ◽  
Author(s):  
Satinderjit Singh
Keyword(s):  
Median Filter ◽  
Computational Cost ◽  
Spatial Coherence ◽  
General Purpose ◽  
Median Filtering ◽  
Basic Algorithm ◽  
Temporal Complexity ◽  
Filter Kernel ◽  
One Step ◽  
High Computational Cost

Median filtering is a commonly used technique in image processing. The main problem of the median filter is its high computational cost (for sorting N pixels, the temporal complexity is O(N·log N), even with the most efficient sorting algorithms). When the median filter must be carried out in real time, the software implementation in general-purpose processorsdoes not usually give good results. This Paper presents an efficient algorithm for median filtering with a 3x3 filter kernel with only about 9 comparisons per pixel using spatial coherence between neighboring filter computations. The basic algorithm calculates two medians in one step and reuses sorted slices of three vertical neighboring pixels. An extension of this algorithm for 2D spatial coherence is also examined, which calculates four medians per step.

Basic set of experiments for determination of mechanical properties of sand

2014 ◽  
Vol 62 (1) ◽  
pp. 129-137
Author(s):  
A. Sawicki ◽  
J. Mierczyński
Keyword(s):  
Mechanical Properties ◽  
Soil Mechanics ◽  
Physical And Mechanical Properties ◽  
Local Strain ◽  
Initial State ◽  
Laboratory Equipment ◽  
Additional Information ◽  
Basic Set ◽  
Initial Anisotropy

Abstract A basic set of experiments for the determination of mechanical properties of sands is described. This includes the determination of basic physical and mechanical properties, as conventionally applied in soil mechanics, as well as some additional experiments, which provide further information on mechanical properties of granular soils. These additional experiments allow for determination of steady state and instability lines, stress-strain relations for isotropic loading and pure shearing, and simple cyclic shearing tests. Unconventional oedometric experiments are also presented. Necessary laboratory equipment is described, which includes a triaxial apparatus equipped with local strain gauges, an oedometer capable of measuring lateral stresses and a simple cyclic shearing apparatus. The above experiments provide additional information on soil’s properties, which is useful in studying the following phenomena: pre-failure deformations of sand including cyclic loading compaction, pore-pressure generation and liquefaction, both static and caused by cyclic loadings, the effect of sand initial anisotropy and various instabilities. An important feature of the experiments described is that they make it possible to determine the initial state of sand, defined as either contractive or dilative. Experimental results for the “Gdynia” model sand are shown.

New Algorithm for Modeling of Bronchial Trees

2012 ◽  
Vol 17 (4) ◽  
pp. 179-190
Author(s):  
Kacper Pluta ◽  
Marcin Janaszewski ◽  
Michał Postolski
Keyword(s):  
Quantitative Analysis ◽  
3D Model ◽  
Ct Images ◽  
Basic Algorithm ◽  
New Model ◽  
Comparison Of Results ◽  
Basic Model ◽  
New Models ◽  
Bronchial Tubes

Abstract The article presents new conception of 3D model of human bronchial tubes, which represents bronchial tubes extracted from CT images of the chest. The new algorithm which generates new model is an extension of the algorithm (basic algorithm) proposed by Hiroko Kitaoka, Ryuji Takaki and Bela Suki. The basic model has been extended by geometric deformations of branches and noise which occur in bronchial trees extracted from CT images. The article presents comparison of results obtained with the use of the new algorithm and the basic one. Moreover, the discussion of usefulness of generated new models for testing of algorithms for quantitative analysis of bronchial tubes based on CT images is also included.

MODELING THE SOUTH ATLANTIC OCEAN FROM MEDIUM TO HIGH RESOLUTION

2014 ◽  
Vol 31 (2) ◽  
Author(s):  
Mariela Gabioux ◽  
Vladimir Santos da Costa ◽  
Joao Marcos Azevedo Correia de Souza ◽  
Bruna Faria de Oliveira ◽  
Afonso De Moraes Paiva
Keyword(s):  
High Resolution ◽  
Atlantic Ocean ◽  
Large Scale ◽  
South Atlantic ◽  
Surface Relaxation ◽  
The South ◽  
Small Surface ◽  
Basic Model ◽  
Basic Set ◽  
Set Up

Results of the basic model configuration of the REMO project, a Brazilian approach towards operational oceanography, are discussed. This configuration consists basically of a high-resolution eddy-resolving, 1/12 degree model for the Metarea V, nested in a medium-resolution eddy-permitting, 1/4 degree model of the Atlantic Ocean. These simulations performed with HYCOM model, aim for: a) creating a basic set-up for implementation of assimilation techniques leading to ocean prediction; b) the development of hydrodynamics bases for environmental studies; c) providing boundary conditions for regional domains with increased resolution. The 1/4 degree simulation was able to simulate realistic equatorial and south Atlantic large scale circulation, both the wind-driven and the thermohaline components. The high resolution simulation was able to generate mesoscale and represent well the variability pattern within the Metarea V domain. The BC mean transport values were well represented in the southwestern region (between Vitória-Trinidade sea mount and 29S), in contrast to higher latitudes (higher than 30S) where it was slightly underestimated. Important issues for the simulation of the South Atlantic with high resolution are discussed, like the ideal place for boundaries, improvements in the bathymetric representation and the control of bias SST, by the introducing of a small surface relaxation. In order to make a preliminary assessment of the model behavior when submitted to data assimilation, the Cooper & Haines (1996) method was used to extrapolate SSH anomalies fields to deeper layers every 7 days, with encouraging results.

Algorithmic Puzzles

2011 ◽  
Author(s):  
Anany Levitin ◽  
Maria Levitin
Keyword(s):  
Problem Solving ◽  
Computer Science ◽  
Algorithm Design ◽  
Divide And Conquer ◽  
Algorithmic Problem ◽  
Design Strategies ◽  
Job Interviews ◽  
Skill Levels ◽  
Problem Solving Skills ◽  
Solution Methods

While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

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