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Dynamic planar convex hull
 Proc. 43rd IEEE Sympos. Found. Comput. Sci
, 2002
"... In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage o ..."
Abstract

Cited by 52 (1 self)
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In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.
Spaceefficient planar convex hull algorithms
 Proc. Latin American Theoretical Informatics
, 2002
"... A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set. ..."
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Cited by 19 (1 self)
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A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set.
Online Zone Construction in Arrangements of Lines in the Plane
 In Proc. of the 3rd Workshop of Algorithm Engineering
, 1999
"... Given a finite set L of lines in the plane we wish to compute the zone of an additional curve fl in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by fl, where fl is not given in advance but rather provided online portion by por ..."
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Cited by 6 (4 self)
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Given a finite set L of lines in the plane we wish to compute the zone of an additional curve fl in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by fl, where fl is not given in advance but rather provided online portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). We implemented the four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms. 1 Introduction Given a finite collection L of lines in the plane, the arrangement A(L) is the subdivision of the plane into vertices, edges and faces induced by L. Arrangements of lines in the plane, as well as arrangements of other objects and in higher dimensional spaces, ...
Optimal inplace planar convex hull algorithms
 Proceedings of Latin American Theoretical Informatics (LATIN 2002), volume 2286 of Lecture Notes in Computer Science
, 2002
"... An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optima ..."
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Cited by 4 (2 self)
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An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optimal, some more so than others...
Online zone construction in arrangements of lines in the plane
 Proc. of the 3rd Workshop of Algorithm Engineering
, 1999
"... Given a finite set L of lines in the plane we wish to compute the zone of an additional curve
in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by
, where
is not given in advance but rather provided online portion by portion. ..."
Abstract

Cited by 1 (0 self)
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Given a finite set L of lines in the plane we wish to compute the zone of an additional curve
in the arrangement A(L), namely the set of faces of the planar subdivision induced by the lines in L that are crossed by
, where
is not given in advance but rather provided online portion by portion. This problem is motivated by the computation of the area bisectors of a polygonal set in the plane. We present four algorithms which solve this problem efficiently and exactly (giving precise results even on degenerate input). Our main algorithm is a novel approach based on the binary plane partition technique. We implemented all four algorithms. We present implementation details, comparison of performance, and a discussion of the advantages and shortcomings of each of the proposed algorithms.
Computing the Center of Area of a Convex Polygon
, 2003
"... The center of area of a convex planar set X is the point... ..."