Mn Processors Research Articles

PCR algorithm for parallel computing the solution of the general restricted linear equations

In this paper we present a parallel algorithm for parallel computing the solution of the general restricted linear equations Ax=b,x∈T, where T is a subspace of ℂn and b∈AT. By this algorithm the solution x=AT,S(2)b is obtained in n(log 2m+log 2(n−s+1)+7)+log 2m+1 steps with P=mn processors when m≥2(n−1) and with P=2n(n−1) processors otherwise.

PCR algorithm for the parallel computation of the solution of a class of singular linear systems

The paper presents a new highly parallel algorithm for computing the solution of a class of singular linear systems WAWx = b , b ∈ R ( ( WA ) k 2 ) , x ∈ R ( ( AW ) k 1 ) . By the algorithm the solution x = A d, W b is obtained in T = m { 7 + ⌈ log 2 n ⌉ + ( 1 + ⌈ log 2 m ⌉ ) 2 + ⌈ log 2 ( m - r + 1 ) ⌉ } + ⌈ log 2 mn ⌉ steps with P = mn processors when n ⩾ 2( m − 1) and with P = 2 m( m − 1) processors otherwise.

PCR algorithm for parallel computing minimum-norm ( T) least-squares ( S) solution of inconsistent linear equations

This paper presents a new highly parallel algorithm for computing the minimum-norm ( T) least-squares ( S) solution of inconsistent linear equations Ax=b(A∈ R m×n r,b∉ R(A)) . By this algorithm the solution x= A S, T + b is obtained in T=(1+ m)(1+log 2 m)+ n(6+log 2( n− r+1)+log 2 m+log 2 n)− r(1+log 2 n) steps with P= mn processors when m⩾2( n−1) and with P=2 n( n−1) processors otherwise.

Finding congruent regions in parallel

Given a straight-line embedded plane graphh G of n edges and a polygon P of m edges, m≤ n, we describe an algorithm for finding all polygons in G that are congruent to P. Our algorithm requires Θ( n log n) time for a CREW PRAM with m processors. This improves upon the O( n 2) time (with m processors) required by the systolic array algorithmm of [7]. We also show the problem is in NC by showing how to implement our algorithm in Θ(log n) time using mn processors.

Parallel clustering algorithms

Clustering techniques play an important role in exploratory pattern analysis, unsupervised learning and image segmentation applications. Many clustering algorithms, both partitional clustering and hierarchical clustering, require intensive computation, even for a modest number of patterns. This paper presents two parallel clustering algorithms. For a clustering problem with N = 2 n patterns and M = 2 m features, the time complexity of the traditional partitional clustering algorithm on a single processor computer is O( MNK), where K is the number of clusters. The proposed algorithm on anSIMD computer with MN processors has a time complexity O( K( n + m)). The time complexity of the proposed single-link hierarchical clustering algorithm is reduced from O( MN 2) of the uniprocessor algorithm to O( nN) with MN processors.