An O((log log n)/sup 2/) time algorithm to compute the convex hull of sorted points on reconfigurable meshes

1998 ◽  
Vol 9 (12) ◽  
pp. 1167-1179 ◽  
Author(s):  
T. Hayashi ◽  
K. Nakano ◽  
S. Olarlu
Keyword(s):  
Convex Hull ◽  
Time Algorithm ◽  
Reconfigurable Meshes

θ(1) time algorithm for 2D convex hull on a reconfigurable mesh computer architecture

2019 ◽  
Vol 13 (24) ◽  
pp. 1165-1180
Author(s):  
Jelloul Elmsbahi ◽  
Mohammed Khaldoun ◽  
Omar Bouattane ◽  
Ahmed Errami
Keyword(s):  
Convex Hull ◽  
Computer Architecture ◽  
Time Algorithm ◽  
Reconfigurable Mesh

IMAGE TEMPLATE MATCHING ON RECONFIGURABLE MESHES

1996 ◽  
Vol 06 (03) ◽  
pp. 345-353 ◽  
Author(s):  
KUO-LIANG CHUNG
Keyword(s):  
Parallel Algorithm ◽  
Template Matching ◽  
Time Algorithm ◽  
Grey Scale ◽  
Reconfigurable Mesh ◽  
Reconfigurable Meshes ◽  
Bus System

A mesh-connected computer enhanced by a reconfigurable bus system is referred to as a reconfigurable mesh (RM). Given an n×n grey-scale image and m×m template, in this paper, an O( log m) time parallel algorithm for template matching is presented on a RM with O(m2n2) processors. Suppose the image and template are binary, an O(1) time algorithm is presented on a RM with O(m3n2) processors. Both algorithms are superior to the best known algorithms on RMs.

LOCATING AN OBNOXIOUS LINE AMONG PLANAR OBJECTS

2012 ◽  
Vol 22 (05) ◽  
pp. 391-405
Author(s):  
DANNY Z. CHEN ◽  
HAITAO WANG
Keyword(s):  
Convex Hull ◽  
Euclidean Distance ◽  
Time Algorithm ◽  
Positive Weight ◽  
Time Solution ◽  
Previous Algorithm ◽  
Minimum Weighted Euclidean Distance ◽  
Improved Algorithm

Given a set P of n points in the plane such that each point has a positive weight, we study the problem of finding an obnoxious line that intersects the convex hull of P and maximizes the minimum weighted Euclidean distance to all points of P. We present an O(n2 log n) time algorithm for the problem, improving the previously best-known O(n2 log 3 n) time solution. We also consider a variant of this problem whose input is a set of m polygons with a total of n vertices in the plane such that each polygon has a positive weight and whose goal is to locate an obnoxious line with respect to the weighted polygons. An O(mn + n log 2 n log m + m2 log n log 2 m) time algorithm for this variant was known previously. We give an improved algorithm of O(mn + n log 2 n + m2 log n) time. Further, we reduce the time bound of a previous algorithm for the case of the problem with unweighted polygons from O((m2 + n log m) log n) to O(m2 + n log m).

A Real-Time Algorithm for Convex Hull Construction and Delaunay Triangulation of Scattered Points Data

2011 ◽  
Vol 181-182 ◽  
pp. 661-666
Author(s):  
Xue Ming He ◽  
Yi Lu ◽  
Cheng Gang Li ◽  
Min Min Ni ◽  
Chen Liang Hua
Keyword(s):  
Data Structure ◽  
Computational Geometry ◽  
Convex Hull ◽  
Surface Reconstruction ◽  
Delaunay Triangulation ◽  
Time Algorithm ◽  
Important Data ◽  
Geometry Design ◽  
Data Points ◽  
Angle Method

Convex hull is a very important data structure of computational geometry design. This paper presents an algorithm to construct the convex hull of a set of scattered points by coordinates and relative angle method. The algorithm determines the convex vertexes and eliminates some non-convex vertexes, which greatly reduces the searching scope and the complexity. Delaunay triangulation is widely used in 3D surface reconstruction. Due to its duality, Delaunay triangulation is usually constructed through Voronoi diagram. Delaunay triangulation is directly constructed in this paper. The algorithm is simple, stable and easy to implement, especially for less data points.

Fast component labelling and convex hull computation on reconfigurable meshes

1993 ◽  
Vol 11 (7) ◽  
pp. 447-455 ◽  
Author(s):  
Stephan Olariu ◽  
James L Schwing ◽  
Jingyuan Zhang
Keyword(s):  
Convex Hull ◽  
Fast Component ◽  
Reconfigurable Meshes ◽  
Convex Hull Computation

An $O(n\log ^2 h)$ Time Algorithm for the Three-Dimensional Convex Hull Problem

1991 ◽  
Vol 20 (2) ◽  
pp. 259-269 ◽  
Author(s):  
Herbert Edelsbrunner ◽  
Weiping Shi
Keyword(s):  
Convex Hull ◽  
Three Dimensional ◽  
Time Algorithm

OPTIMAL TRIANGULATIONS OF POINTS AND SEGMENTS WITH STEINER POINTS

2010 ◽  
Vol 20 (01) ◽  
pp. 89-104 ◽  
Author(s):  
BORIS ARONOV ◽  
TETSUO ASANO ◽  
STEFAN FUNKE
Keyword(s):  
Convex Hull ◽  
Polynomial Time ◽  
Natural Extension ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Optimal Location ◽  
Constant Number ◽  
Steiner Points ◽  
Vertex Set ◽  
Internal Angle

Consider a set X of points in the plane and a set E of non-crossing segments with endpoints in X. One can efficiently compute the triangulation of the convex hull of the points, which uses X as the vertex set, respects E, and maximizes the minimum internal angle of a triangle. In this paper we consider a natural extension of this problem: Given in addition a Steiner pointp, determine the optimal location of p and a triangulation of X ∪ {p} respecting E, which is best among all triangulations and placements of p in terms of maximizing the minimum internal angle of a triangle. We present a polynomial-time algorithm for this problem and then extend our solution to handle any constant number of Steiner points.

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