Lower Bounds

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Kevin Matulef - One of the best experts on this subject based on the ideXlab platform.

  • property testing Lower Bounds via communication complexity
    Conference on Computational Complexity, 2011
    Co-Authors: Eric Blais, Joshua Brody, Kevin Matulef
    Abstract:

    We develop a new technique for proving Lower Bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known Lower Bounds in communication complexity to prove Lower Bounds in testing. This scheme is general and implies a number of new testing Bounds, as well as simpler proofs of several known Bounds. For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a Lower bound of Omega(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010). The same argument behind this Lower bound also implies a new proof of known Lower Bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known Bounds.

Eric Blais - One of the best experts on this subject based on the ideXlab platform.

  • property testing Lower Bounds via communication complexity
    Conference on Computational Complexity, 2011
    Co-Authors: Eric Blais, Joshua Brody, Kevin Matulef
    Abstract:

    We develop a new technique for proving Lower Bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known Lower Bounds in communication complexity to prove Lower Bounds in testing. This scheme is general and implies a number of new testing Bounds, as well as simpler proofs of several known Bounds. For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a Lower bound of Omega(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010). The same argument behind this Lower bound also implies a new proof of known Lower Bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known Bounds.

Emmanuel Neron - One of the best experts on this subject based on the ideXlab platform.

  • OR - Lower Bounds for a multi-skill project scheduling problem
    Operations Research Proceedings, 2012
    Co-Authors: Dhib, Ameur Soukhal, Anis Kooli, Emmanuel Neron
    Abstract:

    The aim of this paper is to present Lower Bounds for a Multi-Skill Project Scheduling Problem, including some classical Lower Bounds and more enhanced ones. Starting from the Lower Bounds found in the literature, we focus on the particularity of our problem and on the adaptation of these Lower Bounds to our problem. We present preliminary results obtained with these new Lower Bounds. The adaptation of the time window adjustments used with energetic reasoning, shows the specificity of this problem, especially slack computation, which requires solving a max-flow with minimum cost problem.

  • Lower Bounds for an industrial multi-skill project scheduling problem
    2011
    Co-Authors: Cheikh Dhib, Anis Kooli, Ameur Soukhal, Emmanuel Neron
    Abstract:

    The aim of this paper is to present Lower Bounds for a Multi-Skill Project Scheduling Problem, including some classical Lower Bounds and more enhanced ones. Starting from the Lower Bounds found in the literature, we focus on the particularity of our problem and on the adaptation of these Lower Bounds to our problem. We present preliminary results obtained with these new Lower Bounds. The adaptation of the time window adjustments used with energetic reasoning, shows the specificity of this problem, especially slack computation, which requires solving a max-flow with minimum cost problem.

  • Lower Bounds for Resource Constrained Project Scheduling Problem
    2006
    Co-Authors: Emmanuel Neron, Christian Artigues, Philippe Baptiste, Jacques Carlier, Jean Damay, Sophie Demassey, Philippe Laborie
    Abstract:

    We review the most recent Lower Bounds for the makespan minimization variant of the Resource Constrained Project Scheduling Problem. Lower Bounds are either based on straight relaxations of the problems (e.g., single machine, parallel machine relaxations) or on constraint programming and/or linear programming formulations of the problem.

Arie M. C. A. Koster - One of the best experts on this subject based on the ideXlab platform.

  • treewidth Lower Bounds with brambles
    European Symposium on Algorithms, 2005
    Co-Authors: Hans L. Bodlaender, Alexander Grigoriev, Arie M. C. A. Koster
    Abstract:

    In this paper we present a new technique for computing Lower Bounds for graph treewidth. Our technique is based on the characterisation of the treewidth as the maximum order of a bramble of the graph. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a Lower bound for the treewidth that is at most a constant factor away from the exact treewidth. For both algorithms, we report on extensive computational experiments that show that the algorithms give often excellent Lower Bounds, in particular when applied to (close to) planar graphs.

  • Treewidth Lower Bounds with Brambles
    2005
    Co-Authors: Hans L. Bodlaender, Alexander Grigoriev, Arie M. C. A. Koster
    Abstract:

    In this paper we present a new technique for computing Lower Bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a Lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum. For both algorithms, we report on extensive computational experiments that show that the algorithms give often excellent Lower Bounds, in particular when applied to (close to) planar graphs.

  • ESA - Treewidth Lower Bounds with brambles
    Algorithms – ESA 2005, 2005
    Co-Authors: Hans L. Bodlaender, Alexander Grigoriev, Arie M. C. A. Koster
    Abstract:

    In this paper we present a new technique for computing Lower Bounds for graph treewidth. Our technique is based on the characterisation of the treewidth as the maximum order of a bramble of the graph. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a Lower bound for the treewidth that is at most a constant factor away from the exact treewidth. For both algorithms, we report on extensive computational experiments that show that the algorithms give often excellent Lower Bounds, in particular when applied to (close to) planar graphs.

  • WEA - Degree-Based treewidth Lower Bounds
    Experimental and Efficient Algorithms, 2005
    Co-Authors: Arie M. C. A. Koster, Thomas Wolle, Hans L. Bodlaender
    Abstract:

    Every Lower bound for treewidth can be extended by taking the maximum of the Lower bound over all subgraphs or minors. This extension is shown to be a very vital idea for improving treewidth Lower Bounds. In this paper, we investigate a total of nine graph parameters, providing Lower Bounds for treewidth. The parameters have in common that they all are the vertex-degree of some vertex in a subgraph or minor of the input graph. We show relations between these graph parameters and study their computational complexity. To allow a practical comparison of the Bounds, we developed heuristic algorithms for those parameters that are N P-hard to compute. Computational experiments show that combining the treewidth Lower Bounds with minors can considerably improve the Lower Bounds.

Joshua Brody - One of the best experts on this subject based on the ideXlab platform.

  • property testing Lower Bounds via communication complexity
    Conference on Computational Complexity, 2011
    Co-Authors: Eric Blais, Joshua Brody, Kevin Matulef
    Abstract:

    We develop a new technique for proving Lower Bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known Lower Bounds in communication complexity to prove Lower Bounds in testing. This scheme is general and implies a number of new testing Bounds, as well as simpler proofs of several known Bounds. For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a Lower bound of Omega(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich (2010). The same argument behind this Lower bound also implies a new proof of known Lower Bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known Bounds.