The VLSI Complexity of Selected Graph Problems
Journal of the ACM (JACM)
Efficient parallel algorithms for a class of graph theoretic problems
SIAM Journal on Computing
Communications of the ACM - Special section on computer architecture
ACM Computing Surveys (CSUR)
Optimal simulations between mesh-connected arrays of processors
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Graph Problems on a Mesh-Connected Processor Array
Journal of the ACM (JACM)
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A reconfigurable and fault-tolerant VLSI multiprocessor array
ISCA '81 Proceedings of the 8th annual symposium on Computer Architecture
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The tree machine: a highly concurrent computing environment
The tree machine: a highly concurrent computing environment
Parallel Processing with the Perfect Shuffle
IEEE Transactions on Computers
On the Structure of the Homogeneous Multiprocessor
IEEE Transactions on Computers
Systolic Arrays with Embedded Tree Structures for Connectivity Problems
IEEE Transactions on Computers
Efficient VLSI Networks for Parallel Processing Based on Orthogonal Trees
IEEE Transactions on Computers
IEEE Transactions on Computers
The Diogenes Approach to Testable Fault-Tolerant Arrays of Processors
IEEE Transactions on Computers
IEEE Transactions on Computers
Systolic Processing and an Implementation for Signal and Image Processing
IEEE Transactions on Computers
Modular Matrix Multiplication on a Linear Array
IEEE Transactions on Computers
IEEE Transactions on Computers
New lower bound techniques for VLSI
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Solving tree problems on a mesh-connected processor array
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Solving some graph problems with optimal or near-optimal speedup on mesh-of-trees networks
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Finding Biconnected Componemts And Computing Tree Functions In Logarithmic Parallel Time
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
A Systolic Design for Connectivity Problems
IEEE Transactions on Computers
On Synthesizing Optimal Family of Linear Systolic Arrays for Matrix Multiplication
IEEE Transactions on Computers
Parallel Architectures and Algorithms for Image Component Labeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Image Processing Algorithms on the Scan Line Array Processor
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Parallel and Distributed Systems
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Parallel algorithms for computing the minimum spanning tree of a weighted undirected graph, and the bridges and articulation points of an undirected graphs on a fixed-size linear array of processors are presented. For a graph of n vertices, the algorithms operate on a linear array of p processors and require O(n2/p) time for all p, 1 = p = n. In particular, using n processors the algorithms require O(n) time which is optimal on this model. The paper describes two approaches to limit the communication requirements for solving the problems. The first is a divide-and-conquer strategy applied to Sollin's algorithm for finding the minimum spanning tree of a graph. The second uses a novel data-reduction technique that constructs an auxiliary graph with no more than 2n - 2 edges, whose bridges and articulation points are the bridges and articulation points of the original graph.