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.

scholarly journals Length of Maximal Common Subsequences

1992 ◽  
Vol 21 (426) ◽  
Author(s):  
Kim Skak Larsen
Keyword(s):  
Dynamic Programming ◽  
Parallel Algorithm ◽  
Linear Time ◽  
Programming Approach ◽  
Simple Modification ◽  
Dynamic Programming Approach ◽  
Pram Model ◽  
Crew Pram ◽  
The Common ◽  
Crcw Pram

<p>The problem of computing the length of the maximal common subsequences of two strings is quite well examined in the sequential case. There are many variations, but the standard approach is to compute the length in quadratic time using dynamic programming. A linear-time parallel algorithm can be obtained via a simple modification of this strategy by letting a linear number of processors sweep through the table created for the dynamic programming approach.</p><p>However, the contribution of this paper is to show that the problem is in NC. More specifically, we show that the length of the maximal common subsequences of two strings <em>s</em> and <em>t</em> can be computed in time O(log |s| € log |t|) in the CREW PRAM model and in time Theta(min(log |s|, log |t|)) in the COMMON CRCW PRAM model.</p>

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.

A SIMPLE PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 437-445 ◽  
Author(s):  
CLIVE N. GALLEY ◽  
COSTAS S. ILIOPOULOS
Keyword(s):  
Parallel Algorithm ◽  
Parallel Computation ◽  
Simple Algorithm ◽  
Partition Problem ◽  
Pram Model ◽  
Single Function ◽  
Crcw Pram

This paper shows a simple algorithm for solving the single function coarsest partition problem on the CRCW PRAM model of parallel computation using O(n) processors in O( log n) time with O(n1+ε) space.

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.

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 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.

scholarly journals Parallel Algorithms for Single-Layer Channel Routing

1997 ◽  
Vol 07 (03) ◽  
pp. 267-277
Author(s):  
Ronald I. Greenberg ◽  
Shih-Chuan Hung ◽  
Jau-Der Shih
Keyword(s):  
Parallel Algorithms ◽  
Linear Time ◽  
Single Layer ◽  
Channel Routing ◽  
Processor Time ◽  
Channel Boundary ◽  
Crew Pram ◽  
Minimum Separation ◽  
Crcw Pram ◽  
River Routing

We provide efficient parallel algorithms for the minimum separation, offset range, and optimal offset problems for single-layer channel routing. We consider all the variations of these problems that are known to have linear-time sequential solutions rather than limiting attention to the "river-routing" context, where single-sided connections are disallowed. For the minimum separation problem, we obtain O( lg N) time on a CREW PRAM or [Formula: see text] time on a (common) CRCW PRAM, both with optimal work (processor-time product) of O(N), where $N$ is the number of terminals. For the offset range problem, we obtain the same time and processor bounds as long as only one side of the channel contains single-sided nets. For the optimal offset problem with single-sided nets on one side of the channel, we obtain time O( lg N lg lg N) on a CREW PRAM or [Formula: see text] time on a CRCW PRAM with O(N lg lg N) work. Not only does this improve on previous results for river routing, but we can obtain an even better time of O(( lg lg N)2) on the CRCW PRAM in the river routing context. In addition, wherever our results allow a channel boundary to contain single-sided nets, the results also apply when that boundary is ragged and N incorporates the number of bendpoints.

AN OPTIMAL RANDOMIZED PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM

1996 ◽  
Vol 06 (02) ◽  
pp. 187-193
Author(s):  
JOSEPH JÁJÁ ◽  
KWAN WOO RYU
Keyword(s):  
Parallel Algorithm ◽  
High Probability ◽  
Rooted Tree ◽  
Partition Problem ◽  
Single Function ◽  
Crew Pram ◽  
Euler Tour ◽  
Crcw Pram

We describe a randomized parallel algorithm to solve the single function coarsest partition problem. The algorithm runs in O( log n) time using O(n) operations with high probability on the Priority CRCW PRAM. The previous best known algorithms run in O( log 2 n) time using O(n log 2 n) operations on the CREW PRAM and O( log n) time using O(n log log n) operations on the Arbitrary CRCW PRAM. The technique presented can be used to generate the Euler tour of a rooted tree optimally from the parent representation.

A PARALLEL ALGORITHM FOR ENCLOSED AND ENCLOSING TRIANGLES

1992 ◽  
Vol 02 (02) ◽  
pp. 191-214 ◽  
Author(s):  
SHARAT CHANDRAN ◽  
DAVID M. MOUNT
Keyword(s):  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Convex Polygon ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
New Techniques ◽  
Crcw Pram

We consider the problems of computing the largest area triangle enclosed within a given n-sided convex polygon and the smallest area triangle which encloses a given convex polygon. We show that these problems are closely related by presenting a single sequential linear time algorithm which essentially solves both problems simultaneously. We also present a cost-optimal parallel algorithm that solves both of these problems in O( log log n) time using n/ log log n processors on a CRCW PRAM. In order to achieve these bounds we develop new techniques for the design of parallel algorithms for computational problems involving the rotating calipers method.

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.

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