The Experts below are selected from a list of 2235 Experts worldwide ranked by ideXlab platform

Debajyoti Mondal - One of the best experts on this subject based on the ideXlab platform.

  • the complexity of drawing a graph in a polygonal Region
    Graph Drawing, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. A special case is the problem of extending a partial planar graph drawing, which was proved NP-hard by Patrignani. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open for a Simply Connected Region.

  • the complexity of drawing a graph in a polygonal Region
    arXiv: Computational Complexity, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. This strengthens an NP-hardness result by Patrignani on extending partial planar graph drawings. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open in the case of a Simply Connected Region. We also show that, even for integer input coordinates, it is possible that drawing a graph in a polygonal Region requires some vertices to be placed at irrational coordinates. By contrast, the coordinates are known to be bounded in the special case of a convex Region, or for drawing a path in any polygonal Region.

Anna Lubiw - One of the best experts on this subject based on the ideXlab platform.

  • the complexity of drawing a graph in a polygonal Region
    Graph Drawing, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. A special case is the problem of extending a partial planar graph drawing, which was proved NP-hard by Patrignani. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open for a Simply Connected Region.

  • the complexity of drawing a graph in a polygonal Region
    arXiv: Computational Complexity, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. This strengthens an NP-hardness result by Patrignani on extending partial planar graph drawings. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open in the case of a Simply Connected Region. We also show that, even for integer input coordinates, it is possible that drawing a graph in a polygonal Region requires some vertices to be placed at irrational coordinates. By contrast, the coordinates are known to be bounded in the special case of a convex Region, or for drawing a path in any polygonal Region.

S B Feodosyev - One of the best experts on this subject based on the ideXlab platform.

  • local vibrational modes in crystal lattices with a Simply Connected Region of the quasi continuous phonon spectrum
    Low Temperature Physics, 2006
    Co-Authors: A V Kotlyar, S B Feodosyev
    Abstract:

    It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a Simply Connected Region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from ...

  • local vibrational modes in crystal lattices with a Simply Connected Region of the quasi continuous phonon spectrum
    Low Temperature Physics, 2006
    Co-Authors: A V Kotlyar, S B Feodosyev
    Abstract:

    It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a Simply Connected Region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from the known values of the local frequencies.

Tillmann Miltzow - One of the best experts on this subject based on the ideXlab platform.

  • the complexity of drawing a graph in a polygonal Region
    Graph Drawing, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. A special case is the problem of extending a partial planar graph drawing, which was proved NP-hard by Patrignani. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open for a Simply Connected Region.

  • the complexity of drawing a graph in a polygonal Region
    arXiv: Computational Complexity, 2018
    Co-Authors: Anna Lubiw, Tillmann Miltzow, Debajyoti Mondal
    Abstract:

    We prove that the following problem is complete for the existential theory of the reals: Given a planar graph and a polygonal Region, with some vertices of the graph assigned to points on the boundary of the Region, place the remaining vertices to create a planar straight-line drawing of the graph inside the Region. This strengthens an NP-hardness result by Patrignani on extending partial planar graph drawings. Our result is one of the first showing that a problem of drawing planar graphs with straight-line edges is hard for the existential theory of the reals. The complexity of the problem is open in the case of a Simply Connected Region. We also show that, even for integer input coordinates, it is possible that drawing a graph in a polygonal Region requires some vertices to be placed at irrational coordinates. By contrast, the coordinates are known to be bounded in the special case of a convex Region, or for drawing a path in any polygonal Region.

A V Kotlyar - One of the best experts on this subject based on the ideXlab platform.

  • local vibrational modes in crystal lattices with a Simply Connected Region of the quasi continuous phonon spectrum
    Low Temperature Physics, 2006
    Co-Authors: A V Kotlyar, S B Feodosyev
    Abstract:

    It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a Simply Connected Region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from ...

  • local vibrational modes in crystal lattices with a Simply Connected Region of the quasi continuous phonon spectrum
    Low Temperature Physics, 2006
    Co-Authors: A V Kotlyar, S B Feodosyev
    Abstract:

    It is shown that the use of the mode classification adopted in the Jacobi matrix method and which is the most natural one for describing localized states leads to extremely rapid convergence of the Green functions for frequencies lying outside the quasi-continuum band of the crystal. This has made it possible to obtain rather general analytical expressions for the conditions of formation and the characteristics of local modes due to the presence of light impurity atoms in crystal lattices having a Simply Connected Region of the quasi-continuous phonon spectrum. The accuracy with which the frequencies and intensities of the local modes are determined using these expressions is illustrated for examples of light substitutional impurities (isotopic and weakly coupled) and close-packed structures (fcc and hcp) and also isolated pairs of isotopic impurities in an fcc crystal lattice. In particular, the results permit simple and extremely accurate evaluation of the parameters of the host lattice and defect from the known values of the local frequencies.