567 research outputs found
Conflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of discs in the plane can
be Conflict-Free colored with a total of at most colors. That is,
it can be colored with colors such that for any (covered) point
there is some disc whose color is distinct from all other colors of discs
containing . They also showed that this bound is asymptotically tight. In
this paper we prove the following stronger results:
\begin{enumerate} \item [(i)] Any set of discs in the plane can be
colored with a total of at most colors such that (a) for any
point that is covered by at least discs, there are at least
distinct discs each of which is colored by a color distinct from all other
discs containing and (b) for any point covered by at most discs,
all discs covering are colored distinctively. We call such a coloring a
{\em -Strong Conflict-Free} coloring. We extend this result to pseudo-discs
and arbitrary regions with linear union-complexity.
\item [(ii)] More generally, for families of simple closed Jordan regions
with union-complexity bounded by , we prove that there exists
a -Strong Conflict-Free coloring with at most colors.
\item [(iii)] We prove that any set of axis-parallel rectangles can be
-Strong Conflict-Free colored with at most colors.
\item [(iv)] We provide a general framework for -Strong Conflict-Free
coloring arbitrary hypergraphs. This framework relates the notion of -Strong
Conflict-Free coloring and the recently studied notion of -colorful
coloring. \end{enumerate}
All of our proofs are constructive. That is, there exist polynomial time
algorithms for computing such colorings
DO MULTI-PLANAR ACL INJURY RISK VARIABLES RANK INDIVIDUALS MORE CONSISTENTLY ACROSS TASKS THAN UNI-PLANAR VARIABLES?
The ACL injury mechanism is multi-planar, yet rarely are multi-planar variables examined in an injury risk context. This study examines if multi-planar variables rank individuals more consistently across multiple tasks than uni-planar variables. Forty-four female athletes performed bilateral drop vertical jumps, single-leg hops, single-leg drop vertical jumps and sidestep tasks on their dominant leg. Uni-planar (KMab) and multi-planar (KMnsag) variables of the knee were extracted and correlated between tasks. Participants was ranked according to KMab and KMnsag, and then grouped into quintiles for each task. When variables are consistently ranked across tasks, a movement signature is identified. In total, uni-planar movement signatures were identified more than multi-planar movement signatures. However, both undesirable multi-planar and uni-planar movement signatures were identified in unique participants. Multi-planar and uni-planar variables are both important when screening for undesirable movements
INITIAL EXPLORATIONS USING THE KNEE MOMENT VECTOR VERSUS THE KNEE ABDUCTION MOMENT TO IDENTIFY ATHLETES AT RISK OF ACL INJURY
The knee abduction moment (KM-Y) is a biomechanical risk factor for ACL injury, yet multi-planar loads are known to strain the ACL. The KM-Y alone is often used for injury screening and prediction. This study examined if the KM-Y alone would identify athletes with high knee moments. Forty five female participants performed a bilateral drop jump and single leg drop jump with each leg and their 3D motion characteristics and ground reaction forces were measured. The identification of “at risk” individuals was compared between KM-Y, the non-sagittal resultant moment and the resultant knee moment using a risk threshold of the mean+1.6SD. The KM-Y identified 60 and 70% athletes in each task whereas also using the non-sagittal resultant moment identified 90 and 100%. This suggests that transverse plane moments should not be ignored to identify at risk athletes
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
We consider the following motion-planning problem: we are given unit
discs in a simple polygon with vertices, each at their own start position,
and we want to move the discs to a given set of target positions. Contrary
to the standard (labeled) version of the problem, each disc is allowed to be
moved to any target position, as long as in the end every target position is
occupied. We show that this unlabeled version of the problem can be solved in
time, assuming that the start and target positions are at
least some minimal distance from each other. This is in sharp contrast to the
standard (labeled) and more general multi-robot motion-planning problem for
discs moving in a simple polygon, which is known to be strongly NP-hard
Searching edges in the overlap of two plane graphs
Consider a pair of plane straight-line graphs, whose edges are colored red
and blue, respectively, and let n be the total complexity of both graphs. We
present a O(n log n)-time O(n)-space technique to preprocess such pair of
graphs, that enables efficient searches among the red-blue intersections along
edges of one of the graphs. Our technique has a number of applications to
geometric problems. This includes: (1) a solution to the batched red-blue
search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an
algorithm to compute the maximum vertical distance between a pair of 3D
polyhedral terrains one of which is convex in O(n log n) time, where n is the
total complexity of both terrains; (3) an algorithm to construct the Hausdorff
Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n)
time and O(n+m) space, where n is the total number of points in all clusters
and m is the number of crossings between all clusters; (4) an algorithm to
construct the farthest-color Voronoi diagram of the corners of n axis-aligned
rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle
problem for n parallel line segments in the plane in optimal O(n log n) time.
All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure
Approximating the Maximum Overlap of Polygons under Translation
Let and be two simple polygons in the plane of total complexity ,
each of which can be decomposed into at most convex parts. We present an
-approximation algorithm, for finding the translation of ,
which maximizes its area of overlap with . Our algorithm runs in
time, where is a constant that depends only on and .
This suggest that for polygons that are "close" to being convex, the problem
can be solved (approximately), in near linear time
Simulation-Based Design of Bicuspidization of the Aortic Valve
Objective: Severe congenital aortic valve pathology in the growing patient
remains a challenging clinical scenario. Bicuspidization of the diseased aortic
valve has proven to be a promising repair technique with acceptable durability.
However, most understanding of the procedure is empirical and retrospective.
This work seeks to design the optimal gross morphology associated with surgical
bicuspidization with simulations, based on the hypothesis that modifications to
the free edge length cause or relieve stenosis.
Methods: Model bicuspid valves were constructed with varying free edge
lengths and gross morphology. Fluid-structure interaction simulations were
conducted in a single patient-specific model geometry. The models were
evaluated for primary targets of stenosis and regurgitation. Secondary targets
were assessed and included qualitative hemodynamics, geometric height,
effective height, orifice area and prolapse.
Results: Stenosis decreased with increasing free edge length and was
pronounced with free edge length less than or equal to 1.3 times the annular
diameter d. With free edge length 1.5d or greater, no stenosis occurred. All
models were free of regurgitation. Substantial prolapse occurred with free edge
length greater than or equal to 1.7d.
Conclusions: Free edge length greater than or equal to 1.5d was required to
avoid aortic stenosis in simulations. Cases with free edge length greater than
or equal to 1.7d showed excessive prolapse and other changes in gross
morphology. Cases with free edge length 1.5-1.6d have a total free edge length
approximately equal to the annular circumference and appeared optimal. These
effects should be studied in vitro and in animal studies
Bounded Model Checking for Probabilistic Programs
In this paper we investigate the applicability of standard model checking
approaches to verifying properties in probabilistic programming. As the
operational model for a standard probabilistic program is a potentially
infinite parametric Markov decision process, no direct adaption of existing
techniques is possible. Therefore, we propose an on-the-fly approach where the
operational model is successively created and verified via a step-wise
execution of the program. This approach enables to take key features of many
probabilistic programs into account: nondeterminism and conditioning. We
discuss the restrictions and demonstrate the scalability on several benchmarks
- …