PARALLEL COMPUTATION OF INTERNAL AND EXTERNAL FARTHEST NEIGHBORS IN SIMPLE POLYGONS

1992 ◽  
Vol 02 (02) ◽  
pp. 175-190 ◽  
Author(s):  
SUMANTA GUHA
Keyword(s):  
Parallel Algorithms ◽  
Parallel Computation ◽  
Shortest Path ◽  
Simple Polygon ◽  
Divide And Conquer ◽  
Simple Polygons ◽  
Crew Pram ◽  
Serial Algorithm

We present efficient parallel algorithms for two problems in simple polygons: the all-farthest neighbors problem and the external all-farthest neighbors problem. The all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ψ(p) in P farthest from p when the distance between p and ψ(p) is measured by the shortest path between them constrained to lie inside P. The external all-farthest neighbors problem is that of computing, for each vertex p of a simple polygon P, a point ϕ(p) on (the boundary of) P farthest from p when the distance between p and ϕ(p) is measured by the shortest path between them constrained to lie outside (the interior of) P. Both our algorithms run in O( log 2 n) time on a CREW PRAM with O(n) processors. Our divide-and-conquer method for the external all-farthest neighbors problem, in fact, leads to a new O(n log n) time serial algorithm that matches the currently best serial algorithm for this problem, but is simpler.

OPTIMAL PARALLEL ALGORITHMS FOR TRIANGULATED SIMPLE POLYGONS

1995 ◽  
Vol 05 (01n02) ◽  
pp. 145-170 ◽  
Author(s):  
JOHN HERSHBERGER
Keyword(s):  
Convex Hull ◽  
Parallel Algorithms ◽  
Shortest Path ◽  
Simple Polygon ◽  
Implicit Representation ◽  
Shortest Path Tree ◽  
Simple Polygons ◽  
Pram Model ◽  
Crew Pram ◽  
Path Queries

We provide optimal parallel solutions to several shortest path and visibility problems set in triangulated simple polygons. Let P be a triangulated simple polygon with n vertices, preprocessed to support shortest path queries. We can find the shortest path tree from any point inside P in O(log n) time using O(n/log n) processors. In the game bounds, we can preprocess P for shooting queries (a query can be answered in O(log n) time by a uniprocessor). Given a set S of m points inside P, we can find an implicit representation of the relative convex hull of S in O(log(nm)) time with O(m) processors. If the relative convex hull has k edges, we can explicitly produce these edges in O(log(nm)) time with O(k/log(nm)) processors. All of these algorithms are deterministic and use the CREW PRAM model.

Determining Weak Visibility of a Polygon from an Edge in Parallel

1998 ◽  
Vol 08 (03) ◽  
pp. 277-304
Author(s):  
Danny Z. Chen
Keyword(s):  
Computational Model ◽  
Parallel Algorithm ◽  
Simple Polygon ◽  
Sequential Algorithms ◽  
Simple Polygons ◽  
Crew Pram

The problem of determining the weak visibility of an n-vertex simple polygon P from an edge e of P is that of deciding whether every point in P is weakly visible from e. In this paper we present an optimal parallel algorithm for solving this problem. Our algorithm runs in O( log n) time using O(n/ log n) processors in the CREW PRAM computational model, and is very different from the sequential algorithms for this problem. We also show how to solve optimally, in parallel, several other problems that are related to the weak visibility of simple polygons.

scholarly journals Query-Points Visibility Constraint Minimum Link Paths in Simple Polygons

2021 ◽  
Vol 182 (3) ◽  
pp. 301-319
Author(s):  
Mohammad Reza Zarrabi ◽  
Nasrollah Moghaddam Charkari
Keyword(s):  
Shortest Path ◽  
Simple Polygon ◽  
Query Point ◽  
Simple Polygons ◽  
Link Distance ◽  
Shortest Path Map ◽  
Number Of Faces

We study the query version of constrained minimum link paths between two points inside a simple polygon P with n vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning P into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points s, t and a query point q. Then, the proposed solution is extended to a general case for three arbitrary query points s, t and q. In the former, we propose an algorithm with O(n) preprocessing time. Extending this approach for the latter case, we develop an algorithm with O(n3) preprocessing time. The link distance of a q-visible path between s, t as well as the path are provided in time O(log n) and O(m + log n), respectively, for the above two cases, where m is the number of links.

PROVABLY FASTEST PARALLEL ALGORITHMS FOR BIPARTITE PERMUTATION GRAPHS

1999 ◽  
Vol 09 (03) ◽  
pp. 385-390 ◽  
Author(s):  
LIN CHEN ◽  
JULIUS Y. JIANG ◽  
MAUNG T. NYEU
Keyword(s):  
Parallel Algorithms ◽  
Shortest Path ◽  
Hamiltonian Path ◽  
Permutation Graphs ◽  
Crew Pram ◽  
Bipartite Permutation Graphs

Provably fastest parallel algorithms for a number of problems on bipartite permutation graphs are presented here. These problems include, among others, connectivity, recognition, isomorphism detection, Hamiltonian path, and shortest path. The algorithms here all run in logarithmic time on CREW PRAM. The processor bound is the same as that for multiplying two matrices in logarithmic time on the model and is subcubic.

FINDING AN OPTIMAL BRIDGE BETWEEN TWO POLYGONS

2002 ◽  
Vol 12 (03) ◽  
pp. 249-261 ◽  
Author(s):  
XUEHOU TAN
Keyword(s):  
Hierarchical Structure ◽  
Shortest Path ◽  
Line Segment ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Search Trees ◽  
Bridge Problem ◽  
Path Queries

Let π(a,b) denote the shortest path between two points a, b inside a simple polygon P, which totally lies in P. The geodesic distance between a and b in P is defined as the length of π(a,b), denoted by gd(a,b), in contrast with the Euclidean distance between a and b in the plane, denoted by d(a,b). Given two disjoint polygons P and Q in the plane, the bridge problem asks for a line segment (optimal bridge) that connects a point p on the boundary of P and a point q on the boundary of Q such that the sum of three distances gd(p′,p), d(p,q) and gd(q,q′), with any p′ ∈ P and any q′ ∈ Q, is minimized. We present an O(n log 3 n) time algorithm for finding an optimal bridge between two simple polygons. This significantly improves upon the previous O(n2) time bound. Our result is obtained by making substantial use of a hierarchical structure that consists of segment trees, range trees and persistent search trees, and a structure that supports dynamic ray shooting and shortest path queries as well.

scholarly journals Identifying Deviations in Microscopic Blood Images using Parallel Computing and Divide and Conquer Image Fragmentation

2020 ◽  
pp. 54-59
Author(s):  
Sudhir Tirumalasetty ◽  
J. Sri Latha ◽  
J. Neeharika ◽  
L. Sri Pravallika ◽  
M. Manasa
Keyword(s):  
Parallel Computing ◽  
Ct Scan ◽  
Shortest Path ◽  
Medical Images ◽  
Specific Area ◽  
Divide And Conquer ◽  
Shortest Path Algorithm ◽  
Microscopic Images ◽  
Patient Diagnosis ◽  
Fungal Identification

Most of the patient diagnosis revolves around in identifying abnormalities in their respective medical images. These images are of various types, likely Ultrasound, CT scan, MRI and microscopic images like bio-chemical slides, micro-biological slides & pathological slides. Few abnormalities are fractures, bad cells in blood, tumors, fungal identification etc. Finding the abnormal portions in these images needs expertise by the physician; this apt identification promotes and guarantees healthy medication by the physician or surgeon to patient. In medical microscopic images normal portions and abnormal portions are mixed together. None of the abnormal portions are related to abnormal and normal portions of image i.e. deviations are scattered among normal portions of image. These deviations are not present in some portions for specific area in the images. None of these deviations are overlapped nor can be grouped together into a single portion physically in the image. Deviations are isolated along with normal portions of images. Identifying such deviations is vital. In previous methods these deviations are identified used BFS and Shortest Path Algorithm. This paper focuses on identifying deviations using parallel computing applied over fragmented portions of blood images using divide and conquer.

scholarly journals AN OPTIMAL PARALLEL ALGORITHM FOR DETECTING WEAK VISIBILITY OF A SIMPLE POLYGON

1995 ◽  
Vol 05 (01n02) ◽  
pp. 93-124 ◽  
Author(s):  
DANNY Z. CHEN
Keyword(s):  
Computational Model ◽  
Parallel Algorithm ◽  
Simple Polygon ◽  
Sequential Algorithms ◽  
Crew Pram

The problem of detecting the weak visibility of an n-vertex simple polygon P is that of finding whether P is weakly visible from one of its edges and (if it is) identifying every edge from which P is weakly visible. In this paper, we present an optimal parallel algorithm for solving this problem. Our algorithm runs in O(log n) time using O(n/log n) processors in the CREW PRAM computational model, and is very different from the sequential algorithms for this problem. Based on this algorithm, several other problems related to weak visibility can be optimally solved in parallel.

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

2014 ◽  
Vol 644-650 ◽  
pp. 1891-1894
Author(s):  
Li Juan Wang ◽  
An Sheng Deng ◽  
Bo Jiang ◽  
Qi Wei
Keyword(s):  
Test Data ◽  
Shortest Path ◽  
Time Complexity ◽  
Simple Polygon ◽  
Rubber Band ◽  
Crossing Over ◽  
Euclidean Shortest Path ◽  
Adjacent Segments ◽  
Improved Algorithm

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

LOGARITHMIC-TIME LINK PATH QUERIES IN A SIMPLE POLYGON

1995 ◽  
Vol 05 (04) ◽  
pp. 369-395 ◽  
Author(s):  
ESTHER M. ARKIN ◽  
JOSEPH S.B. MITCHELL ◽  
SUBHASH SURI
Keyword(s):  
Data Structure ◽  
Shortest Path ◽  
Simple Polygon ◽  
Additive Constant ◽  
Time And Space ◽  
Link Distance ◽  
Path Distance ◽  
Path Queries ◽  
Shortest Path Distance ◽  
Small Additive

We develop a data structure for answering link distance queries between two arbitrary points in a simple polygon. The data structure requires O(n3) time and space for its construction and answers link distance queries in O(log n) time, after which a minimum-link path can be reported in time proportional to the number of links. Here, n denotes the number of vertices of the polygon. Our result extends to link distance queries between pairs of segments or polygons. We also propose a simpler data structure for computing a link distance approximately, where the error is bounded by a small additive constant. Finally, we also present a scheme for approximating the link and the shortest path distance simultaneously.

Sign in / Sign up

Export Citation Format

Share Document