20,678 research outputs found
Schnyder woods for higher genus triangulated surfaces, with applications to encoding
Schnyder woods are a well-known combinatorial structure for plane
triangulations, which yields a decomposition into 3 spanning trees. We extend
here definitions and algorithms for Schnyder woods to closed orientable
surfaces of arbitrary genus. In particular, we describe a method to traverse a
triangulation of genus and compute a so-called -Schnyder wood on the
way. As an application, we give a procedure to encode a triangulation of genus
and vertices in bits. This matches the worst-case
encoding rate of Edgebreaker in positive genus. All the algorithms presented
here have execution time , hence are linear when the genus is fixed.Comment: 27 pages, to appear in a special issue of Discrete and Computational
Geometr
Quantum Hall Ground States, Binary Invariants, and Regular Graphs
Extracting meaningful physical information out of a many-body wavefunction is
often impractical. The polynomial nature of fractional quantum Hall (FQH)
wavefunctions, however, provides a rare opportunity for a study by virtue of
ground states alone. In this article, we investigate the general properties of
FQH ground state polynomials. It turns out that the data carried by an FQH
ground state can be essentially that of a (small) directed graph/matrix. We
establish a correspondence between FQH ground states, binary invariants and
regular graphs and briefly introduce all the necessary concepts. Utilizing
methods from invariant theory and graph theory, we will then take a fresh look
on physical properties of interest, e.g. squeezing properties, clustering
properties, etc. Our methodology allows us to `unify' almost all of the
previously constructed FQH ground states in the literature as special cases of
a graph-based class of model FQH ground states, which we call \emph{accordion}
model FQH states
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
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