941 research outputs found
Topological Stability of Kinetic -Centers
We study the -center problem in a kinetic setting: given a set of
continuously moving points in the plane, determine a set of (moving)
disks that cover at every time step, such that the disks are as small as
possible at any point in time. Whereas the optimal solution over time may
exhibit discontinuous changes, many practical applications require the solution
to be stable: the disks must move smoothly over time. Existing results on this
problem require the disks to move with a bounded speed, but this model is very
hard to work with. Hence, the results are limited and offer little theoretical
insight. Instead, we study the topological stability of -centers.
Topological stability was recently introduced and simply requires the solution
to change continuously, but may do so arbitrarily fast. We prove upper and
lower bounds on the ratio between the radii of an optimal but unstable solution
and the radii of a topologically stable solution---the topological stability
ratio---considering various metrics and various optimization criteria. For we provide tight bounds, and for small we can obtain nontrivial
lower and upper bounds. Finally, we provide an algorithm to compute the
topological stability ratio in polynomial time for constant
Spatial information retrieval and geographical ontologies: an overview of the SPIRIT project
A large proportion of the resources available on the world-wide
web refer to information that may be regarded as geographically
located. Thus most activities and enterprises take place in one or
more places on the Earth's surface and there is a wealth of survey
data, images, maps and reports that relate to specific places or
regions. Despite the prevalence of geographical context, existing
web search facilities are poorly adapted to help people find
information that relates to a particular location. When the name of
a place is typed into a typical search engine, web pages that
include that name in their text will be retrieved, but it is likely
that many resources that are also associated with the place may
not be retrieved. Thus resources relating to places that are inside
the specified place may not be found, nor may be places that are
nearby or that are equivalent but referred to by another name.
Specification of geographical context frequently requires the use
of spatial relationships concerning distance or containment for
example, yet such terminology cannot be understood by existing
search engines. Here we provide a brief survey of existing
facilities for geographical information retrieval on the web, before
describing a set of tools and techniques that are being developed
in the project SPIRIT : Spatially-Aware Information Retrieval on
the Internet (funded by European Commission Framework V
Project IST-2001-35047)
Guest Editor's Foreword (Special Issue with Selected Papers from the 19th International Symposium on Graph Drawing, GD 2011)
This issue of the Journal of Graph Algorithms and Applications is devoted to the nineteenth International Symposium on Graph Drawing, held September 19-21, 2011, in Eindhoven, the Netherlands
Higher order Delaunay triangulations
For a set P of points in the plane, we introduce a class of triangulations that is an
extension of the Delaunay triangulation. Instead of requiring that for each triangle the
circle through its vertices contains no points of P inside, we require that at most k points
are inside the circle. Since there are many different higher-order Delaunay triangulations
for a point set, other useful criteria for triangulations can be incorporated without sacrificing
the well-shapedness too much. Applications include realistic terrain modelling and
mesh generation
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