scholarly journals Constant Time Algorithms for Computing the Contour of Maximal Elements on a Reconfigurable Mesh

1998 ◽  
Vol 08 (03) ◽  
pp. 351-361 ◽  
Author(s):  
M. Manzur Murshed ◽  
Richard P. Brent
Keyword(s):  
Parallel Architectures ◽  
Constant Time ◽  
Maximal Elements ◽  
Reconfigurable Mesh ◽  
Constant Time Algorithms

There has recently been an interest in the introduction of reconfigurable buses to existing parallel architectures. Among them the Reconfigurable Mesh (RM) draws much attention because of its simplicity. This paper presents three constant time algorithms to compute the contour of the maximal elements of N planar points on the RM. The first algorithm employs an RM of size N × N while the second one uses a 3-D RM of size [Formula: see text]. We further extend the result to k-D RM of size N1/(k - 1) × N1/(k - 1) × … × N1/(k - 1).

Tighter and Broader Complexity Results for Reconfigurable Models

1998 ◽  
Vol 08 (03) ◽  
pp. 271-282 ◽  
Author(s):  
Jerry L. Trahan ◽  
Anu G. Bourgeois ◽  
Ramachandran Vaidyanathan
Keyword(s):  
Fast Algorithms ◽  
Constant Time ◽  
Complexity Classes ◽  
Complexity Results ◽  
Reconfigurable Mesh ◽  
Bounded Complexity

A number of models allow processors to reconfigure their local connections to create and alter various bus configurations. This reconfiguration enables development of fast algorithms for fundamental problems, many in constant time. We investigate the ability of such models by relating time and processor bounded complexity classes defined for these models to each other and to those of more traditional models. In this work, (1) we tighten the relations for some of the models, placing them more precisely in relation to each other than was previously known (particularly, the Linear Reconfigurable Network and Directed Reconfigurable Network relative to circuit-defined classes), and (2) we include models (Fusing-Restricted Reconfigurable Mesh and Pipelined Reconfigurable Mesh) not previously considered.

scholarly journals Multiplication of Matrices With Different Sparseness Properties on Dynamically Reconfigurable Meshes

VLSI Design ◽  
1999 ◽  
Vol 9 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Martin Middendorf ◽  
Hartmut Schmeck ◽  
Heiko Schröder ◽  
Gavin Turner
Keyword(s):  
Lower Bound ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
The Other ◽  
Constant Time ◽  
Dynamically Reconfigurable ◽  
Reconfigurable Meshes ◽  
Constant Time Algorithms

Algorithms for multiplying several types of sparse n x n-matrices on dynamically reconfigurable n x n-arrays are presented. For some classes of sparse matrices constant time algorithms are given, e.g., when the first matrix has at most kn elements in each column or in each row and the second matrix has at most kn nonzero elements in each row, where k is a constant. Moreover, O(kn ) algorithms are obtained for the case that one matrix is a general sparse matrix with at most kn nonzero elements and the other matrix has at most k nonzero elements in every row or in every column. Also a lower bound of Ω(Kn ) is proved for this and other cases which shows that the algorithms are close to the optimum.

EFFICIENT REBALANCING OF B-TREES WITH RELAXED BALANCE

1996 ◽  
Vol 07 (02) ◽  
pp. 169-186 ◽  
Author(s):  
KIM S. LARSEN ◽  
ROLF FAGERBERG
Keyword(s):  
Shared Memory ◽  
Parallel Architectures ◽  
Constant Time ◽  
Maximal Size ◽  
Long Run ◽  
B Trees ◽  
The Common ◽  
Logarithmic Number ◽  
Asynchronous Parallel

B-trees with relaxed balance have been defined to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating so that extensive locking can be avoided in connection with updates. We analyze B-trees with relaxed balance, and prove that each update gives rise to at most [loga(N/2)]+1 rebalancing operations, where a is the degree of the B-tree, and N is the bound on its maximal size since it was last in balance. Assuming that the size of nodes is at least twice the degree, we prove that rebalancing can be performed in amortized constant time. So, in the long run, rebalancing is constant time on average, even if any particular update could give rise to a logarithmic number of rebalancing operations. We also prove that the amount of rebalancing done at any particular level decreases exponentially going from the leaves towards the root. This is important since the higher up in the tree a lock due to a rebalancing operation occurs, the larger a subtree which cannot be accessed by other processes for the duration of that lock. All of these results are in fact obtained for the more general (a, b)-trees, so we have results for both of the common B-tree versions as well as 2-3 trees and 2-3-4 trees.

A CONSTANT TIME SORTING ALGORITHM FOR A THREE DIMENSIONAL RECONFIGURABLE MESH AND RECONFIGURABLE NETWORK

1995 ◽  
Vol 05 (03) ◽  
pp. 401-412 ◽  
Author(s):  
MARK S. MERRY ◽  
JOHNNIE BAKER
Keyword(s):  
Computer Science ◽  
Real Number ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Constant Time ◽  
Sorting Algorithm ◽  
Compression Algorithms ◽  
Reconfigurable Mesh ◽  
Integer Sorting ◽  
Time Selection

Sorting techniques have numerous applications in computer science. Current real number and integer sorting techniques for the reconfigurable mesh operate in constant time using a reconfigurable mesh of size n × n to sort n numbers. This paper presents a constant time algorithm to sort n items on a reconfigurable network with [Formula: see text] switches and [Formula: see text] processors. Also, new constant time selection and compression algorithms are given. All results may also be implemented on the 3-D reconfigurable mesh.

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