A parallel algorithm for constructing Voronoi diagrams based on point-set adaptive grouping

2013 ◽  
Vol 26 (2) ◽  
pp. 434-446 ◽  
Author(s):  
Jiechen Wang ◽  
Can Cui ◽  
Yikang Rui ◽  
Liang Cheng ◽  
Yingxia Pu ◽  
...  
Keyword(s):  
Parallel Algorithm ◽  
Voronoi Diagrams ◽  
Point Set

An optimal expected-time parallel algorithm for Voronoi diagrams

1988 ◽  
pp. 190-198 ◽  
Author(s):  
Christos Levcopoulos ◽  
Jyrki Katajainen ◽  
Andrzej Lingas
Keyword(s):  
Parallel Algorithm ◽  
Voronoi Diagrams ◽  
Expected Time

A FAST PARALLEL ALGORITHM FOR FINDING THE CONVEX HULL OF A SORTED POINT SET

1996 ◽  
Vol 06 (02) ◽  
pp. 231-241 ◽  
Author(s):  
OMER BERKMAN ◽  
BARUCH SCHIEBER ◽  
UZI VISHKIN
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Parallel Algorithm ◽  
Divide And Conquer ◽  
Trivial Extension ◽  
Running Time ◽  
Point Set ◽  
Crcw Pram

We present a parallel algorithm for finding the convex hull of a sorted point set. The algorithm runs in O( log log n) (doubly logarithmic) time using n/ log log n processors on a Common CRCW PRAM. To break the Ω( log n/ log log n) time barrier required to output the convex hull in a contiguous array, we introduce a novel data structure for representing the convex hull. The algorithm is optimal in two respects: (1) the time-processor product of the algorithm, which is linear, cannot be improved, and (2) the running time, which is doubly logarithmic, cannot be improved even by using a linear number of processors. The algorithm demonstrates the power of the “the divide-and-conquer doubly logarithmic paradigm” by presenting a non-trivial extension to situations that previously were known to have only slower algorithms.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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