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 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 An Efficient Parallel Algorithm for the Single Function Coarsest Partition Problem on the EREW PRAM

ETRI Journal ◽  
1999 ◽  
Vol 21 (2) ◽  
pp. 22-30
Author(s):  
Kyeoung-Ju Ha Ha ◽  
Kyo-Min Ku Ku ◽  
Hae-Kyeong Park Park ◽  
Young-Kook Kim Kim ◽  
Kwan-Woo Ryu Ryu
Keyword(s):  
Parallel Algorithm ◽  
Partition Problem ◽  
Erew Pram ◽  
Single Function

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>

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.

ON FINDING EULER TOURS IN PARALLEL

1993 ◽  
Vol 03 (03) ◽  
pp. 223-231 ◽  
Author(s):  
EDSON N. CACERES ◽  
NARSINGH DEO ◽  
SHIVAKUMAR SASTRY ◽  
JAYME L. SZWARCFITER
Keyword(s):  
Parallel Algorithm ◽  
Spanning Tree ◽  
Intermediate Step ◽  
Euler Tour ◽  
Euler Tours

We describe an alternative implementation of Atallah and Vishkin’s parallel algorithm for finding an Euler Tour of a graph. Instead of finding a spanning tree as an intermediate step, this algorithm is based on identifying a strut which is easier to compute. Using the strut, vertices which have more than one circuit passing through them are identified directly. Stitching at such vertices reduces the number of circuits in the Euler Partition.

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