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.

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.

PARALLEL ALGORITHMS FOR LONGEST INCREASING CHAINS IN THE PLANE AND RELATED PROBLEMS

1999 ◽  
Vol 09 (04) ◽  
pp. 511-520 ◽  
Author(s):  
MIKHAIL J. ATALLAH ◽  
DANNY Z. CHEN ◽  
KEVIN S. KLENK
Keyword(s):  
Parallel Algorithms ◽  
Computational Model ◽  
Parallel Algorithm ◽  
Related Problem ◽  
Single Source ◽  
Crew Pram ◽  
Longest Paths ◽  
Nonnegative Weight

Given a set [Formula: see text] of n points in the plane such that each point in [Formula: see text] is asscociated with a nonnegative weight, we consider the problem of computing the single-source longest increasing chains among the points in [Formula: see text] This problem is a generalization of the plannar maximal layers problem. In this paper, we present a parallel algorithm that computes the single-source longest incresing chains in the plane in [Formula: see text] time using [Formula: see text] processors in the CREW PRAM computational model. We also solve a related problem of computing the all-pairs longest paths in an n-node weighted planar st-graph, in [Formula: see text] time using [Formula: see text] CREW PRAM processors. Both of our parallel algorithms are improvement over the previously best known results.

A parallel algorithm for solving the n-queens problem based on inspired computational model

Biosystems ◽  
2015 ◽  
Vol 131 ◽  
pp. 22-29 ◽  
Author(s):  
Zhaocai Wang ◽  
Dongmei Huang ◽  
Jian Tan ◽  
Taigang Liu ◽  
Kai Zhao ◽  
...  
Keyword(s):  
Computational Model ◽  
Parallel Algorithm

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.

TREE OPEN EAR DECOMPOSITION IN PARALLEL GRAPH ALGORITHMS

1995 ◽  
Vol 05 (02) ◽  
pp. 129-138
Author(s):  
LOUIS IBARRA ◽  
DANA RICHARDS
Keyword(s):  
Parallel Algorithm ◽  
Graph Algorithms ◽  
Depth First Search ◽  
Parallel Graph Algorithms ◽  
Crew Pram ◽  
Np Complete ◽  
Ear Decomposition ◽  
Parallel Graph

Tree open ear decomposition has been proposed as a potentially useful technique in parallel graph algorithms. We present an efficient parallel algorithm implementing depth-first search in a graph, given its tree open ear decomposition. The algorithm runs in O( log n) time with O(m) processors on the CREW PRAM, where m is the number of edges in the graph. We also show that the problem of computing such a decomposition is NP-complete, demonstrating the limited utility of the technique.

Parallel Algorithms for Listing Well-Formed Parentheses Strings

1998 ◽  
Vol 08 (01) ◽  
pp. 19-28 ◽  
Author(s):  
Vincent Vajnovszki ◽  
Jean Pallo
Keyword(s):  
Parallel Algorithms ◽  
Computational Model ◽  
Shared Memory ◽  
Linear Array ◽  
Lexicographic Order ◽  
Memory Location ◽  
Constant Delay ◽  
Crew Pram

We present two cost-optimal parallel algorithms generating the set of all well-formed parentheses strings of length 2n with constant delay for each generated string. In our first algorithm we generate in lexicographic order well-formed parentheses strings represented by bitstrings, and in the second one we use the representation by weight sequences. In both cases the computational model is based on an architecture CREW PRAM, where each processor performs the same algorithm simultaneously on a different set of data. Different processors can access the shared memory at the same time to read different data in the same or different memory locations, but no two processors are allowed to write into the same memory location simultaneously. These results complete a recent parallel generating algorithm for well-formed parentheses strings in a linear array of processors model, due to Akl and Stojmenović.

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