A PROCESSOR EFFICIENT CONNECTIVITY ALGORITHM ON RANDOM GRAPHS

In this paper we present a randomized parallel algorithm for finding the connected components of a random input graph with n vertices in which the edges are chosen with probability p such that [Formula: see text]. The algorithm has O(log2 n) expected time using only O(n) processors on the EREW PRAM model. The probability that the output of our algorithm is correct is at least 1–0.6k, where k is a constant.

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EFFICIENT PARALLEL SHUFFLE RECOGNITION

Parallel Processing Letters ◽

10.1142/s0129626494000429 ◽

1994 ◽

Vol 04 (04) ◽

pp. 455-463 ◽

Cited By ~ 3

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.

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

Parallel Processing Letters ◽

10.1142/s0129626400000275 ◽

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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PARALLEL SEARCH AND MULTISEARCH IN MATRICES WITH SORTED COLUMNS

Parallel Processing Letters ◽

10.1142/s0129626499000530 ◽

1999 ◽

Vol 09 (04) ◽

pp. 575-586

Author(s):

AMIT JAIN

Keyword(s):

Parallel Algorithm ◽

Sequential Algorithm ◽

Parallel Search ◽

Erew Pram ◽

Pram Model ◽

Small Elements

In this paper we consider the problem of searching, and ranking, in an m × n matrix with sorted columns on the EREW PRAM model. We propose a work-optimal parallel algorithm, based on the technique of accelerated cascading, that runs in O( lg m lg lg m)-time for small elements with rank k ≤ m and in O( lg m lg lg m lg (k/m))-time otherwise. Then we show how to improve the parallel-searching algorithm to run in O( lg m lg * lg m))-time with optimal work for small elements (with rank k ≤ m) and in O( lg m lg * ( lg m) lg (k/m))-time with optimal work for large elements (m < k ≤ mn). Next we present a sequential algorithm for multisearch in a matrix with sorted columns. Finally we present a parallel multisearch algorithm that is a generalization of the sequential multisearch algorithm and has a nontrivial dependence on the ranks of the search-elements as well as on the number of search-elements.

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

Parallel Processing Letters ◽

10.1142/s0129626404001763 ◽

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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SUB-LOGARITHMIC ALGORITHMS FOR THE LARGEST EMPTY RECTANGLE PROBLEM

Parallel Processing Letters ◽

10.1142/s0129626493000113 ◽

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.

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MATCHING POLYNOMIALS OF SERIES-PARALLEL GRAPHS

Parallel Processing Letters ◽

10.1142/s0129626493000034 ◽

1993 ◽

Vol 03 (01) ◽

pp. 13-18 ◽

Cited By ~ 2

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.

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

ETRI Journal ◽

10.4218/etrij.99.0199.0203 ◽

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

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A SIMPLE PARALLEL ALGORITHM FOR THE SINGLE FUNCTION COARSEST PARTITION PROBLEM

Parallel Processing Letters ◽

10.1142/s0129626494000405 ◽

1994 ◽

Vol 04 (04) ◽

pp. 437-445 ◽

Cited By ~ 1

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.

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