PARALLEL ALGORITHMS FOR COMPUTING THE CLOSEST VISIBLE VERTEX PAIR BETWEEN TWO POLYGONS

1992 ◽  
Vol 02 (02) ◽  
pp. 135-162 ◽  
Author(s):  
F.R. HSU ◽  
R.C. CHANG ◽  
R.C.T. LEE
Keyword(s):  
Parallel Algorithms ◽  
Pram Model ◽  
Crew Pram

In this paper, we are concerned with the closest visible vertex pair problem, which is defined as follows: we are given two simple non-intersecting polygons P and Q with m and n vertices respectively, we are asked to find a closest visible pair of vertices between P and Q. We shall show that we can solve this problem in O( log (m+n)) time with O(m+n) processors in the CREW PRAM model.

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.

PARALLEL ALGORITHMS FOR MULTIDIMENSIONAL IMAGE TEMPLATE MATCHING

1994 ◽  
Vol 08 (02) ◽  
pp. 457-464
Author(s):  
A. SAOUDI ◽  
M. NIVAT
Keyword(s):  
Parallel Algorithms ◽  
Pattern Matching ◽  
Efficient Algorithm ◽  
Template Matching ◽  
Optimal Algorithms ◽  
Pram Model ◽  
Crew Pram ◽  
Multidimensional Array

This paper presents efficient and optimal parallel algorithms for multidimensional image template matching on CREW PRAM model. For an Nd image and an Md window, we present an optimal (respectively efficient) algorithm which runs in O(log(M)) time with O(Md×Nd/log(M) processors (respectively O(Md×Nd)). We also present efficient and optimal algorithms for solving the multidimensional array and pattern matching.

PARALLEL ALGORITHMS FOR HAMILTONIAN 2-SEPARATOR CHORDAL GRAPHS

2002 ◽  
Vol 12 (01) ◽  
pp. 51-64 ◽  
Author(s):  
B. S. PANDA ◽  
VIJAY NATARAJAN ◽  
SAJAL K. DAS
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Hamiltonian Cycle ◽  
Chordal Graph ◽  
Chordal Graphs ◽  
Pram Model ◽  
Crew Pram ◽  
Crcw Pram

In this paper we propose a parallel algorithm to construct a one-sided monotone polygon from a Hamiltonian 2-separator chordal graph. The algorithm requires O( log n) time and O(n) processors on the CREW PRAM model, where n is the number of vertices and m is the number of edges in the graph. We also propose parallel algorithms to recognize Hamiltonian 2-separator chordal graphs and to construct a Hamiltonian cycle in such a graph. They run in O( log 2 n) time using O(mn) processors on the CRCW PRAM model and O( log 2 n) time using O(m) processors on the CREW PRAM model, respectively.

SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM

1993 ◽  
Vol 03 (01) ◽  
pp. 79-85
Author(s):  
STEPHAN OLARIU ◽  
WENHUI SHEN ◽  
LARRY WILSON
Keyword(s):  
Parallel Algorithms ◽  
Erew Pram ◽  
Pram Model ◽  
The Common ◽  
Crcw Pram ◽  
Natural Way

We show that the Largest Empty Rectangle problem can be solved by reducing it, in a natural way, to the All Nearest Smaller Values problem. We provide two classes of algorithms: the first one assumes that the input points are available sorted by x (resp. y) coordinate. Our algorithm corresponding to this case runs in O(log log n) time using [Formula: see text] processors in the Common-CRCW-PRAM model. For unsorted input, we present algorithms that run in [Formula: see text] time using [Formula: see text] processors in the Common-CRCW-PRAM, or in O( log n) time using [Formula: see text] processors in the EREW-PRAM model. No sub-logarithmic time parallel algorithms have been previously reported for this problem.

scholarly journals SEQUENTIAL AND PARALLEL ALGORITHMS FOR THE k CLOSEST PAIRS PROBLEM

1995 ◽  
Vol 05 (03) ◽  
pp. 273-288 ◽  
Author(s):  
HANS-PETER LENHOF ◽  
MICHIEL SMID
Keyword(s):  
Decision Tree ◽  
Parallel Algorithms ◽  
Dimensional Space ◽  
Decision Tree Model ◽  
Sequential Algorithm ◽  
Tree Model ◽  
Parallel Time ◽  
Parallel Version ◽  
Pram Model ◽  
Crcw Pram

Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and [Formula: see text]. A new and simpler proof is given of Salowe’s theorem, i.e., a sequential algorithm is given that computes the k closest pairs in the set S in O(n log n+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. Salowe’s algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM model. This version runs in O((log n)2 log log n) expected parallel time and has an O(n log n log log n+k) time-processor product. Finally, actual running times are given of an implementation of our sequential algorithm.

The Queue-Read Queue-Write PRAM Model: Accounting for Contention in Parallel Algorithms

1998 ◽  
Vol 28 (2) ◽  
pp. 733-769 ◽  
Author(s):  
Phillip B. Gibbons ◽  
Yossi Matias ◽  
Vijaya Ramachandran
Keyword(s):  
Parallel Algorithms ◽  
Pram Model

THREE TECHNIQUES FOR PARALLEL MAINTENANCE OF A MINIMUM SPANNING TREE UNDER BATCH OF UPDATES

1996 ◽  
Vol 06 (02) ◽  
pp. 213-222 ◽  
Author(s):  
PAOLO FERRAGINA ◽  
FABRIZIO LUCCIO
Keyword(s):  
Data Structure ◽  
Parallel Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Undirected Graph ◽  
Batch Size ◽  
Insertions And Deletions ◽  
Erew Pram ◽  
Pram Model ◽  
Proper Values

In this paper we provide three simple techniques to maintain in parallel the minimum spanning tree of an undirected graph under single or batch of edge updates (i.e., insertions and deletions). Our results extend the use of the sparsification data structure to the EREW PRAM model. For proper values of the batch size, our algorithms require less time and work than the best known dynamic parallel algorithms.

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.

Parallel Algorithms for Recognizing P5-free and ${\bar P}_5$-free Weakly Chordal Graphs

2004 ◽  
Vol 14 (01) ◽  
pp. 119-129
Author(s):  
Stavros D. Nikolopoulos ◽  
Leonidas Palios
Keyword(s):  
Parallel Algorithms ◽  
Chordal Graphs ◽  
Input Graph ◽  
Model Of Computation ◽  
Erew Pram ◽  
Recognition Algorithms ◽  
Pram Model

We prove algorithmic characterizations of weakly chordal graphs, which lead to efficient parallel algorithms for recognizing P5-free and [Formula: see text]-free weakly chordal graphs. For an input graph on n vertices and m edges, our algorithms run in O( log 2n) time and require O(m2/ log n) processors on the EREW PRAM model of computation. The proposed recognition algorithms efficiently detect P5 s and [Formula: see text] in weakly chordal graphs in O( log n) time with O(m2/ log n) processors on the EREW PRAM. Additionally, we show how the algorithms can be augmented to provide a certificate for the existence of a P5 (or a [Formula: see text]) in case the input graph is not P5-free (respectively, [Formula: see text]-free) weakly chordal.

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