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

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.

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.

MATCHING POLYNOMIALS OF SERIES-PARALLEL GRAPHS

1993 ◽  
Vol 03 (01) ◽  
pp. 13-18 ◽  
Author(s):  
LIH-HSING HSU
Keyword(s):  
Parallel Algorithm ◽  
Efficient Algorithm ◽  
Matching Polynomial ◽  
Erew Pram ◽  
Parallel Graph

We present an efficient algorithm for computing the matching polynomial of a series-parallel graph in O(n2) time. This algorithm improves on the previous result of O(n3). We also present a cost-optimal parallel algorithm for computing the matching polynomial of a series-parallel graph using an EREW PRAM computer with the number of processors p less than n2/ log n.

EFFICIENT PARALLEL SHUFFLE RECOGNITION

1994 ◽  
Vol 04 (04) ◽  
pp. 455-463 ◽  
Author(s):  
M. NIVAT ◽  
G.D.S. RAMKUMAR ◽  
C. PANDU RANGAN ◽  
A. SAOUDI ◽  
R. SUNDARAM
Keyword(s):  
Parallel Algorithm ◽  
Erew Pram ◽  
Pram Model

This paper presents a parallel algorithm for verifying that a string X is formed by the shuffle of two strings Y and Z. The algorithm runs in O(log2n) time with O(n2/log2 n) processors on the EREW-PRAM model.

PARALLEL ALGORITHMS FOR FINDING MAXIMAL k-DEPENDENT SETS AND MAXIMAL f-MATCHINGS

1993 ◽  
Vol 04 (02) ◽  
pp. 179-192 ◽  
Author(s):  
KRZYSZTOF DIKS ◽  
OSCAR GARRIDO ◽  
ANDRZEJ LINGAS
Keyword(s):  
Positive Integer ◽  
Parallel Algorithms ◽  
Parallel Algorithm ◽  
Erew Pram

Let k be a positive integer, a subset Q of the set of vertices of a graph G is k-dependent in G if each vertex of Q has no more than k neighbours in Q. We present a parallel algorithm which computes a maximal k-dependent set in a graph on n nodes in time O( log 4 n) on an EREW PRAM with O(n2) processors. In this way, we establish the membership of the problem of constructing a maximal k-dependent set in the class NC. Our algorithm can be easily adapted to compute a maximal k-dependent set in a graph of bounded valence in time O( log * n) using only O(n) EREW PRAM processors. Let f be a positive integer function defined on the set V of vertices of a graph G. A subset F of the set of edges of G is said to be an f-matching if every vertex vɛV is adjacent to at most f(v) edges in-F. We present the first NC algorithm for constructing a maximal f-matching. For a graph on n nodes and m edges the algorithm runs in time O( log 4 n) and uses O(n+m) EREW PRAM processors. For graphs of constantly bounded valence, we can construct a maximal f-matching in O( log * n) time on an EREW PRAM with O(n) processors.

ON FINDING A HAMILTONIAN PATH IN A TOURNAMENT USING SEMI-HEAP

2000 ◽  
Vol 10 (04) ◽  
pp. 279-294
Author(s):  
JIE WU
Keyword(s):  
Data Structure ◽  
Parallel Algorithm ◽  
Ordered Set ◽  
Hamiltonian Path ◽  
Linear Ordering ◽  
Sorting Algorithm ◽  
Ranking System ◽  
Special Linear ◽  
Erew Pram ◽  
Pram Model

The problem of sorting an intransitive total ordered set, a generalization of regular sorting, is considered. This generalized sorting is based on the fact that there exists a special linear ordering (also called a generalized sorted sequence) for any intransitive total ordered set, or equivalently, the existence of a Hamiltonian path in a tournament. A new data structure called semi-heap is proposed to construct an optimal Θ(n log n) sorting algorithm. We also provide a cost-optimal parallel algorithm using semi-heap. The run time of this algorithm is Θ(n) with Θ( log n) processors under the EREW PRAM model. The use of a Hamiltonian path (generalized sorting sequence) as an approximation of a ranking system in a tournament is also discussed.

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