An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations
Journal of the ACM (JACM)
A Survey of Parallel Machine Organization and Programming
ACM Computing Surveys (CSUR)
Computing connected components on parallel computers
Communications of the ACM
Sorting on a mesh-connected parallel computer
Communications of the ACM
Fast parallel sorting algorithms
Communications of the ACM
An efficient data structure for dynamic memory management
Journal of Systems and Software
Complexity of Sequential and Parallel Numerical Algorithms
Complexity of Sequential and Parallel Numerical Algorithms
Parallel algorithms for the transitive closure and the connected component problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Synchronous parallel computation.
Synchronous parallel computation.
ACM Computing Surveys (CSUR)
Optimal parallel generation of a computation tree form
ACM Transactions on Programming Languages and Systems (TOPLAS) - Lecture notes in computer science Vol. 174
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
New Connectivity and MSF Algorithms for Shuffle-Exchange Network and PRAM
IEEE Transactions on Computers
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
A parallel algorithm for computing minimum spanning trees
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Fast connected components algorithms for the EREW PRAM
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
An optimal randomized logarithmic time connectivity algorithm for the EREW PRAM (extended abstract)
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Parallel Constant-Time Connectivity Algorithms on a Reconfigurable Network of Processors
IEEE Transactions on Parallel and Distributed Systems
An efficient and fast parallel-connected component algorithm
Journal of the ACM (JACM)
An Efficient Parallel Recognition Algorithm For Bipartite-Permutation Graphs
IEEE Transactions on Parallel and Distributed Systems
Finding minimum spanning forests in logarithmic time and linear work using random sampling
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes
IEEE Transactions on Parallel and Distributed Systems
On Parallel Algorithms for Single-Fault Diagnosis in Fault Propagation Graph Systems
IEEE Transactions on Parallel and Distributed Systems
Finding connected components in O(log n loglog n) time on the EREW PRAM
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
I/O-complexity of graph algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Concurrent threads and optimal parallel minimum spanning trees algorithm
Journal of the ACM (JACM)
Parallel implementation of an efficient microcode compaction algorithm
ACM SIGMICRO Newsletter
Fully Dynamic Maintenance of k-Connectivity in Parallel
IEEE Transactions on Parallel and Distributed Systems
Cache-oblivious priority queue and graph algorithm applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Efficient Algorithms for List Ranking and for Solving Graph Problems on the Hypercube
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
Improving the efficiency of parallel minimum spanning tree algorithms
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Parallel Algortithms for Hamiltonian 2-Separator Chordal Graphs
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
On External-Memory MST, SSSP, and Multi-way Planar Graph Separation
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
A Functional Approach to External Graph Algorithms
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
On external-memory MST, SSSP and multi-way planar graph separation
Journal of Algorithms
An O(log n log log n) space algorithm for undirected st-connectivity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A fast, parallel spanning tree algorithm for symmetric multiprocessors (SMPs)
Journal of Parallel and Distributed Computing
On the parallel computation of the biconnected and strongly connected co-components of graphs
Discrete Applied Mathematics
An Optimal Parallel Algorithm for Constructing a Spanning Forest on Trapezoid Graphs
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Algorithms for memory hierarchies: advanced lectures
Algorithms for memory hierarchies: advanced lectures
Improving parallel computation with fast integer sorting
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Computing connected components of simple undirected graphs based on generalized rough sets
Knowledge-Based Systems
CC-MR --- finding connected components in huge graphs with mapreduce
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
A comparative study of parallel algorithms for the girth problem
AusPDC '12 Proceedings of the Tenth Australasian Symposium on Parallel and Distributed Computing - Volume 127
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We study parallel algorithms for a number of graph problems, using the Single Instruction Stream-Multiple Data Stream model. We assume that the processors have access to a common memory and that no memory or data alignment time penalties are incurred. We derive a general time bound for a parallel algorithm that uses K processors for finding the connected components of an undirected graph. In particular, an O(log2 n) time bound can be achieved using only K = n⌈n/log2 n⌉ processors. This result is optimal in the sense that the speedup ratio is linear with the number of processors used. The algorithm can also be modified to solve a whole class of graph problems with the same time bound and fewer processors than previous parallel methods.