Computing the $$L_1$$ Geodesic Diameter and Center of a Polygonal Domain
نویسندگان
چکیده
منابع مشابه
Computing the L1 Geodesic Diameter and Center of a Polygonal Domain
For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L1 geodesic diameter in O(n2 + h4) time and the L1 geodesic center in O((n4 + n2h4)α(n)) time, respectively, where α(·) denotes the inverse Ackermann function. No algorithms were known for these problems before. For the Euclidean counterpart, the best algorithms compute the geodesic diameter in...
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We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n ) for any > 0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(n log n)-time algorithm is known by Pollack et al. ...
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This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), it is known that the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this pa...
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A polygonal domain P with n corners V and h holes is a connected polygonal region of genus h whose boundary consists of h + 1 closed chains of n total line segments. The holes and the outer boundary of P are regarded as obstacles. Then, the geodesic distance d(p, q) between any two points p, q in polygonal domain P is defined to be the (Euclidean) length of a shortest obstacle-avoiding path bet...
متن کاملGeodesic diameter of a polygonal domain in O(n^4 log n) time
We show that the geodesic diameter of a polygonal domain with n vertices can be computed in O(n logn) time by considering O(n) candidate diameter endpoints; the endpoints are a subset of vertices of the overlay of shortest path maps from vertices of the domain.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9841-z