Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R 2, and let R be a set of n line segments in R 2 . We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R. To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R2, and let O be a set of disjoint polygonal obstacles in R2. We study the problem of approximating the probability that p and q can see each other; i.e., that the segment connecting p and q does not cross any obstacle in O. To solve this problem, we first approximate each density function by a weighted set of polygons. Then we focus on computing the visibility between two points inside two of such polygons, where we can assume that the points are drawn uniformly at random. We show how this problem can be solved exactly in O((n+m)2) time, where n and m are the total complexities of the two polygons and the set of obstacles, respectively. Using this as a subroutine, we show that the probability that p and q can see each other amidst a set of obstacles of total complexity m can be approximated within error ε in O(1/ε3+m2/ε2) time

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R 2 , and let O be a set of disjoint polygonal obstacles in R 2 . We study the problem of approximating the probability that p and q can see each other; i.e., that the segment connecting p and q does not cross any obstacle in O. To solve this problem, we first approximate each density function by a weighted set of polygons. Then we focus on computing the visibility between two points inside two of such polygons, where we can assume that the points are drawn uniformly at random. We show how this problem can be solved exactly in O((n+ m) 2 ) time, where n and m are the total complexities of the two polygons and the set of obstacles, respectively. Using this as a subroutine, we show that the probability that p and q can see each other amidst a set of obstacles of total complexity m can be approximated within error ε in O(1 / ε 3 + m 2 / ε 2 ) time

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

In this paper we present new geometric algorithms for approximating the visibility between two imprecise locations amidst a set of obstacles, where the imprecise locations are modeled by continuous probability distributions. Our techniques are based on approximating distributions by a set of regions rather than on approximating by a discrete point sample. In this way we obtain guaranteed error bounds, and the results are more robust than similar results based on discrete point sets. We implemented our techniques and present an experimental evaluation. The experiments show that the actual error of our region-based approximation scheme converges quickly when increasing the complexity of the regions

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

\u3cp\u3e Let p and q be two imprecise points, given as probability density functions on R \u3csup\u3e2\u3c/sup\u3e , and let O be a set of disjoint polygonal obstacles in R \u3csup\u3e2\u3c/sup\u3e . We study the problem of approximating the probability that p and q can see each other; i.e., that the segment connecting p and q does not cross any obstacle in O. To solve this problem, we first approximate each density function by a weighted set of polygons. Then we focus on computing the visibility between two points inside two of such polygons, where we can assume that the points are drawn uniformly at random. We show how this problem can be solved exactly in O((n+ m) \u3csup\u3e2\u3c/sup\u3e ) time, where n and m are the total complexities of the two polygons and the set of obstacles, respectively. Using this as a subroutine, we show that the probability that p and q can see each other amidst a set of obstacles of total complexity m can be approximated within error ε in O(1 / ε \u3csup\u3e3\u3c/sup\u3e + m \u3csup\u3e2\u3c/sup\u3e / ε \u3csup\u3e2\u3c/sup\u3e ) time. \u3c/p\u3

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R2, and let O be a set of disjoint polygonal obstacles in R2. We study the problem of approximating the probability that p and q can see each other; i.e., that the segment connecting p and q does not cross any obstacle in O. To solve this problem, we first approximate each density function by a weighted set of polygons. Then we focus on computing the visibility between two points inside two of such polygons, where we can assume that the points are drawn uniformly at random. We show how this problem can be solved exactly in O((n+m)2) time, where n and m are the total complexities of the two polygons and the set of obstacles, respectively. Using this as a subroutine, we show that the probability that p and q can see each other amidst a set of obstacles of total complexity m can be approximated within error ε in O(1/ε3+m2/ε2) time

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as prob- ability density functions on R 2 , and let R be a set of n line segments in R 2 . We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R . To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometryPeer Reviewe

Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

Let p and q be two imprecise points, given as probability density functions on R2 , and let O be a set of disjoint polygonal obstacles in R2 . We study the problem of approximating the probability that p and q can see each other; i.e., that the segment connecting p and q does not cross any obstacle in O . To solve this problem, we first approximate each density function by a weighted set of polygons. Then we focus on computing the visibility between two points inside two of such polygons, where we can assume that the points are drawn uniformly at random. We show how this problem can be solved exactly in O((n+m)2) time, where n and m are the total complexities of the two polygons and the set of obstacles, respectively. Using this as a subroutine, we show that the probability that p and q can see each other amidst a set of obstacles of total complexity m can be approximated within error e in O(1/e3+m2/e2) time.Peer Reviewe