Journal ArticleDOI
Notes on 'divide-and-conquer-based optimal parallel algorithms for some graph problems on EREW PRAM model'
Sajal K. Das,Narsingh Deo +1 more
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Using an exclusive-read and exclusive-write (EREW) parallel random-access memory (PRAM) model with a fixed number of processors, optimal parallel algorithms are presented for several problems on undirected graphs, achieving optimal speedup for dense as well as sparse graphs.Abstract:
Using an exclusive-read and exclusive-write (EREW) parallel random-access memory (PRAM) model with a fixed number of processors, optimal parallel algorithms are presented for several problems on undirected graphs. These problems include finding the connected components, a spanning forest, a fundamental cycle set, the bridges, and checking bipartiteness of a given graph. The algorithms for computing the connected components and a spanning forest are designed using the divide-and-conquer strategy and are used in turn to design efficient algorithms for the remaining three problems. Each of the algorithms achieves optimal speedup for dense as well as sparse graphs, and is optimally scalable up to a certain number of processors. A lower bound on the processor-(time)/sup 2/ product for each algorithm is derived. The input graph is represented by an unordered list of edges, and the use of simple and elegant data structures avoids memory read-conflicts or write-conflicts. >read more
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References
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Depth-First Search and Linear Graph Algorithms
TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.
Journal ArticleDOI
An O(logn) parallel connectivity algorithm
Yossi Shiloach,Uzi Vishkin +1 more
TL;DR: It is conjectured that the barrier of O(log n) cannot be surpassed by any polynomial number of processors and that this performance cannot be achieved in the weaker model.
Book
An Efficient Parallel Biconnectivity Algorithm
Robert E. Tarjan,Uzi Vishkin +1 more
TL;DR: A new algorithm for finding the blocks (biconnected components) of an undirected graph and a general algorithmic technique that simplifies and improves computation of various functions on trees is introduced.
Journal ArticleDOI
Computing connected components on parallel computers
TL;DR: A parallel algorithm which uses n=2 processors to find the connected components of an undirected graph with n vertices in time in time O(n), which can be used to finding the transitive closure of a symmetric Boolean matrix.
Journal ArticleDOI
Efficient parallel algorithms for some graph problems
TL;DR: A general time bound is derived for a parallel algorithm that uses K processors for finding the connected components of an undirected graph and the result is optimal in the sense that the speedup ratio is linear with the number of processors used.