The Experts below are selected from a list of 31374 Experts worldwide ranked by ideXlab platform

Victor Lagerkvist - One of the best experts on this subject based on the ideXlab platform.

  • An initial study of time complexity in Infinite-Domain constraint satisfaction
    Artificial Intelligence, 2017
    Co-Authors: Peter Jonsson, Victor Lagerkvist
    Abstract:

    Abstract The constraint satisfaction problem (CSP) is a widely studied problem with numerous applications in computer science and artificial intelligence. For Infinite-Domain CSPs, there are many results separating tractable and NP-hard cases while upper and lower bounds on the time complexity of hard cases are virtually unexplored. Hence, we initiate a study of the worst-case time complexity of such CSPs. We analyze backtracking algorithms and determine upper bounds on their time complexity. We present asymptotically faster algorithms based on enumeration techniques and we show that these algorithms are applicable to well-studied problems in, for instance, temporal reasoning. Finally, we prove non-trivial lower bounds applicable to many interesting CSPs, under the assumption that certain complexity-theoretic assumptions hold. The gap between upper and lower bounds is in many cases surprisingly small, which suggests that our upper bounds cannot be significantly improved.

  • CP - Upper and Lower Bounds on the Time Complexity of Infinite-Domain CSPs
    Lecture Notes in Computer Science, 2015
    Co-Authors: Peter Jonsson, Victor Lagerkvist
    Abstract:

    The constraint satisfaction problem (CSP) is a widely studied problem with numerous applications in computer science. For Infinite-Domain CSPs, there are many results separating tractable and NP-hard cases while upper bounds on the time complexity of hard cases are virtually unexplored. Hence, we initiate a study of the worst-case time cmplexity of such CSPs. We analyse backtracking algorithms and show that they can be improved by exploiting sparsification. We present even faster algorithms based on enumerating finite structures. Last, we prove non-trivial lower bounds applicable to many interesting CSPs, under the assumption that the strong exponential-time hypothesis is true.

Peter Jonsson - One of the best experts on this subject based on the ideXlab platform.

  • An initial study of time complexity in Infinite-Domain constraint satisfaction
    Artificial Intelligence, 2017
    Co-Authors: Peter Jonsson, Victor Lagerkvist
    Abstract:

    Abstract The constraint satisfaction problem (CSP) is a widely studied problem with numerous applications in computer science and artificial intelligence. For Infinite-Domain CSPs, there are many results separating tractable and NP-hard cases while upper and lower bounds on the time complexity of hard cases are virtually unexplored. Hence, we initiate a study of the worst-case time complexity of such CSPs. We analyze backtracking algorithms and determine upper bounds on their time complexity. We present asymptotically faster algorithms based on enumeration techniques and we show that these algorithms are applicable to well-studied problems in, for instance, temporal reasoning. Finally, we prove non-trivial lower bounds applicable to many interesting CSPs, under the assumption that certain complexity-theoretic assumptions hold. The gap between upper and lower bounds is in many cases surprisingly small, which suggests that our upper bounds cannot be significantly improved.

  • CP - Upper and Lower Bounds on the Time Complexity of Infinite-Domain CSPs
    Lecture Notes in Computer Science, 2015
    Co-Authors: Peter Jonsson, Victor Lagerkvist
    Abstract:

    The constraint satisfaction problem (CSP) is a widely studied problem with numerous applications in computer science. For Infinite-Domain CSPs, there are many results separating tractable and NP-hard cases while upper bounds on the time complexity of hard cases are virtually unexplored. Hence, we initiate a study of the worst-case time cmplexity of such CSPs. We analyse backtracking algorithms and show that they can be improved by exploiting sparsification. We present even faster algorithms based on enumerating finite structures. Last, we prove non-trivial lower bounds applicable to many interesting CSPs, under the assumption that the strong exponential-time hypothesis is true.

Michael M Rogers - One of the best experts on this subject based on the ideXlab platform.

  • spectral methods for the navier stokes equations with one Infinite and two periodic directions
    Journal of Computational Physics, 1991
    Co-Authors: Philippe R Spalart, Robert D Moser, Michael M Rogers
    Abstract:

    Abstract Two numerical methods were designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers (method A, semi-Infinite Domain) and mixing layers or wakes (method B, fully-Infinite Domain). Their originality lies in the use of rapidly-decaying spectral basis functions to approximate the vertical dependence of the solutions, combined with one (method A) or two (method B) slowly-decaying “extra functions” for each wave-vector that exactly represent the irrotational component of the solution at large distances. Both methods eliminate the pressure term as part of the formulation, thus avoiding fractional-step time integration. They yield rapid convergence and are free of spurious modes in the Orr-Sommerfeld spectra. They are also efficient, although the operation count is of order N 2 ( N is the number of modes in the Infinite direction). These methods have been used for extensive direct numerical simulations of transition and turbulence. A new time-integration scheme, with low storage requirements and good stability properties, is also described.

Yang Xiang - One of the best experts on this subject based on the ideXlab platform.

  • a coupled interpolating meshfree method for computing sound radiation in Infinite Domain
    International Journal for Numerical Methods in Engineering, 2018
    Co-Authors: Yang Xiang
    Abstract:

    Summary In this paper, the coupling of the improved interpolating element-free Galerkin (IIEFG) method and the variable-order Infinite acoustic wave envelope element (WEE) method is studied. A coupled IIEFG-WEE method for computing sound radiation is proposed to make use of their advantages while evading their disadvantages. The coupling is achieved by constructing the hybrid shape function of continuity and compatibility on the interface between the IIEFG and WEE Domains. In the IIEFG Domain, the improved interpolating moving least-squares (IIMLS) method is employed to form the shape functions satisfying the Kronecker delta condition while nonsingular weight functions can be used. The impacts of the size of the influence Domain and the shape parameter on the performance of this coupled method are investigated. The numerical results show that the coupled IIEFG-WEE method can take full advantage of both the IIEFG and WEE methods, and that it not only can achieve higher accuracy but also has a faster convergence speed than the conventional method of the finite element coupled with the WEE. The experimental results show that the method is very flexible for acoustic radiation prediction in the Infinite Domain. This article is protected by copyright. All rights reserved.

  • Calculation of sound radiation in Infinite Domain using a meshless method
    The Journal of the Acoustical Society of America, 2016
    Co-Authors: Yang Xiang
    Abstract:

    A meshless method coupling with a variable order Infinite acoustic wave envelope element for sound radiation calculation in Infinite Domain is presented with the aim of accurately calculating the acoustic radiation and improving computational efficiency. It is based on using the element-free Galerkin method in the inner region enclosing the radiator and a variable order Infinite acoustic wave envelope element in the outer region for the proper modeling of the pressure amplitude decay. The details are provided for the derivation and implementation of this method. The factors of influencing the performance of the method, which include the shape function constructing, the number of integration points, the weight functions, and the support Domain, are discussed. A hybrid adaptive Gauss-Legendre quadrature is devised to obtain good integration accuracy. The suitable radius of the support Domain for the acoustic field calculation in free space is also determined by use of numerical experiments. A complex struct...

Manuel Bodirsky - One of the best experts on this subject based on the ideXlab platform.

  • topology is relevant in a dichotomy conjecture for Infinite Domain constraint satisfaction problems
    Logic in Computer Science, 2019
    Co-Authors: Manuel Bodirsky, Michael Pinsker, Miroslav Olsak, Antoine Mottet, Jakub Oprsal, Ross Willard
    Abstract:

    The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (Infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template has a pseudo-Siggers polymorphism, and NP-complete otherwise. One of the important questions related to this conjecture is whether, similarly to the case of finite structures, the condition of having a pseudo-Siggers polymorphism can be replaced by the condition of having polymorphisms satisfying a fixed set of identities of height 1, i.e., identities which do not contain any nesting of functional symbols. We provide a negative answer to this question by constructing for each non-trivial set of height 1 identities a structure whose polymorphisms do not satisfy these identities, but whose CSP is tractable nevertheless. An equivalent formulation of the dichotomy conjecture characterizes tractability of the CSP via the local satisfaction of nontrivial height 1 identities by polymorphisms of the structure. We show that local satisfaction and global satisfaction of nontrivial height 1 identities differ for $\omega$ -categorical structures with less than double exponential orbit growth, thereby resolving one of the main open problems in the algebraic theory of such structures.

  • CSL - Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains
    2018
    Co-Authors: Manuel Bodirsky, Marcello Mamino, Caterina Viola
    Abstract:

    Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite Domains has been classified in this sense. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite Domain. We initiate the systematic investigation of Infinite-Domain VCSPs by studying the complexity of VCSPs for piecewise linear homogeneous cost functions. We remark that in this paper the Infinite Domain will always be the set of rational numbers. We show that such VCSPs can be solved in polynomial time when the cost functions are additionally submodular, and that this is indeed a maximally tractable class: adding any cost function that is not submodular leads to an NP-hard VCSP.

  • Complexity Classification in Infinite-Domain Constraint Satisfaction
    arXiv: Computational Complexity, 2012
    Co-Authors: Manuel Bodirsky
    Abstract:

    A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values to the variables. Depending on the type of constraints that we allow in the input, a CSP might be tractable, or computationally hard. In recent years, general criteria have been discovered that imply that a CSP is polynomial-time tractable, or that it is NP-hard. Finite-Domain CSPs have become a major common research focus of graph theory, artificial intelligence, and finite model theory. It turned out that the key questions for complexity classification of CSPs are closely linked to central questions in universal algebra. This thesis studies CSPs where the variables can take values from an Infinite Domain. This generalization enhances dramatically the range of computational problems that can be modeled as a CSP. Many problems from areas that have so far seen no interaction with constraint satisfaction theory can be formulated using Infinite Domains, e.g. problems from temporal and spatial reasoning, phylogenetic reconstruction, and operations research. It turns out that the universal-algebraic approach can also be applied to study large classes of Infinite-Domain CSPs, yielding elegant complexity classification results. A new tool in this thesis that becomes relevant particularly for Infinite Domains is Ramsey theory. We demonstrate the feasibility of our approach with two complete complexity classification results: one on CSPs in temporal reasoning, the other on a generalization of Schaefer's theorem for propositional logic to logic over graphs. We also study the limits of complexity classification, and present classes of computational problems provably do not exhibit a complexity dichotomy into hard and easy problems.

  • CSL - Collapsibility in Infinite-Domain quantified constraint satisfaction
    Computer Science Logic, 2006
    Co-Authors: Manuel Bodirsky, Hubie Chen
    Abstract:

    In this article, we study the quantified constraint satisfaction problem (QCSP) over Infinite Domains. We develop a technique called collapsibility that allows one to give strong complexity upper bounds on the QCSP. This technique makes use of both logical and universal-algebraic ideas. We give applications illustrating the use of our technique.