384 research outputs found
On interference among moving sensors and related problems
We show that for any set of points moving along "simple" trajectories
(i.e., each coordinate is described with a polynomial of bounded degree) in
and any parameter , one can select a fixed non-empty
subset of the points of size , such that the Voronoi diagram of
this subset is "balanced" at any given time (i.e., it contains points
per cell). We also show that the bound is near optimal even for
the one dimensional case in which points move linearly in time. As
applications, we show that one can assign communication radii to the sensors of
a network of moving sensors so that at any given time their interference is
. We also show some results in kinetic approximate range
counting and kinetic discrepancy. In order to obtain these results, we extend
well-known results from -net theory to kinetic environments
Lower bounds for Arrangement-based Range-Free Localization in Sensor Networks
Colander are location aware entities that collaborate to determine
approximate location of mobile or static objects when beacons from an object
are received by all colanders that are within its distance . This model,
referred to as arrangement-based localization, does not require distance
estimation between entities, which has been shown to be highly erroneous in
practice. Colander are applicable in localization in sensor networks and
tracking of mobile objects.
A set is an -colander if by placing
receivers at the points of , a wireless device with transmission radius
can be localized to within a circle of radius . We present tight
upper and lower bounds on the size of -colanders. We measure the
expected size of colanders that will form -colanders if they
distributed uniformly over the plane
On Strong Centerpoints
Let be a set of points in and be a
family of geometric objects. We call a point a strong centerpoint of
w.r.t if is contained in all that
contains more than points from , where is a fixed constant. A
strong centerpoint does not exist even when is the family of
halfspaces in the plane. We prove the existence of strong centerpoints with
exact constants for convex polytopes defined by a fixed set of orientations. We
also prove the existence of strong centerpoints for abstract set systems with
bounded intersection
Polychromatic Coloring for Half-Planes
We prove that for every integer , every finite set of points in the plane
can be -colored so that every half-plane that contains at least
points, also contains at least one point from every color class. We also show
that the bound is best possible. This improves the best previously known
lower and upper bounds of and respectively. We also show
that every finite set of half-planes can be colored so that if a point
belongs to a subset of at least of the half-planes then
contains a half-plane from every color class. This improves the best previously
known upper bound of . Another corollary of our first result is a new
proof of the existence of small size \eps-nets for points in the plane with
respect to half-planes.Comment: 11 pages, 5 figure
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