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.

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

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.

PARALLEL SEARCH AND MULTISEARCH IN MATRICES WITH SORTED COLUMNS

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.

A Simple Optimal Parallel Algorithm for Reporting Paths in a Tree

1997 ◽  
Vol 07 (01) ◽  
pp. 3-11 ◽  
Author(s):  
Andrzej Lingas ◽  
Anil Maheshwari
Keyword(s):  
Parallel Algorithm ◽  
Random Access ◽  
Input Tree ◽  
Single Pair ◽  
Random Access Machine ◽  
Erew Pram ◽  
Parallel Random Access Machine ◽  
Path Queries

We present optimal parallel solutions to reporting paths between pairs of nodes in an n-node tree. Our algorithms are deterministic and designed to run on an exclusive read exclusive write parallel random-access machine (EREW PRAM). In particular, we provide a simple optimal parallel algorithm for preprocessing the input tree such that the path queries can be answered efficiently. Our algorithm for preprocessing runs in O( log n) time using O(n/ log n) processors. Using the preprocessing, we can report paths between k node pairs in O( log n + log k) time using O(k + (n + S)/ log n) processors on an EREW PRAM, where S is the size of the output. In particular, we can report the path between a single pair of distinct nodes in O( log n) time using O(L/ log n) processors, where L denotes the length of the path.

TREE OPEN EAR DECOMPOSITION IN PARALLEL GRAPH ALGORITHMS

1995 ◽  
Vol 05 (02) ◽  
pp. 129-138
Author(s):  
LOUIS IBARRA ◽  
DANA RICHARDS
Keyword(s):  
Parallel Algorithm ◽  
Graph Algorithms ◽  
Depth First Search ◽  
Parallel Graph Algorithms ◽  
Crew Pram ◽  
Np Complete ◽  
Ear Decomposition ◽  
Parallel Graph

Tree open ear decomposition has been proposed as a potentially useful technique in parallel graph algorithms. We present an efficient parallel algorithm implementing depth-first search in a graph, given its tree open ear decomposition. The algorithm runs in O( log n) time with O(m) processors on the CREW PRAM, where m is the number of edges in the graph. We also show that the problem of computing such a decomposition is NP-complete, demonstrating the limited utility of the technique.

EFFICIENT ALGORITHMS FOR THE EUCLIDEAN DISTANCE TRANSFORM

1995 ◽  
Vol 05 (02) ◽  
pp. 205-212 ◽  
Author(s):  
SANDY PAVEL ◽  
SELIM G. AKL
Keyword(s):  
Parallel Algorithm ◽  
Euclidean Distance ◽  
Sequential Algorithm ◽  
Distance Transform ◽  
Binary Images ◽  
Euclidean Distance Transform ◽  
Erew Pram ◽  
Time Optimal ◽  
Time Bounds ◽  
And Robotics

The Euclidean Distance Transform is an important computational tool for the processing of binary images, with applications in many areas such as computer vision, pattern recognition and robotics. We investigate the properties of this transform and describe an O(n2) time optimal sequential algorithm. A deterministic EREW-PRAM parallel algorithm which runs in O( log n) time using O(n2) processors and O(n2) space is also derived. Further, a cost optimal randomized parallel algorithm which runs within the same time bounds with high probability, is given.

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