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 obstacl...

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Vydané v:	Algorithmica Ročník 81; číslo 7; s. 2682 - 2715
Hlavní autori:	Buchin, Kevin, Kostitsyna, Irina, Löffler, Maarten, Silveira, Rodrigo I.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.07.2019 Springer Nature B.V
Predmet:	35 Partial differential equations 35R Miscellaneous topics involving partial differential equations 60 Probability theory and stochastic processes 60G Stochastic processes Algorithm Analysis and Problem Complexity Algorithms Anàlisi matemàtica Barriers Classificació AMS Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Differential equations, Partial Equacions en derivades parcials Estadística matemàtica Gaussian distribution Matemàtiques i estadística Mathematics of Computing Polygons Probability density functions Probability distribution Processos estocàstics Stochastic processes Theory of Computation Visibility Visibility in polygonal domains Àrees temàtiques de la UPC Gaussian distribution Visibility in polygonal domains Probability distribution
ISSN:	0178-4617, 1432-0541
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-019-00551-2