Finding strongly connected components in distributed graphs
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TLDR
The implementation of a recently proposed parallel algorithm that finds strongly connected components in distributed graphs, and how it is used in a radiation transport solver is described.About:
This article is published in Journal of Parallel and Distributed Computing.The article was published on 2005-08-01 and is currently open access. It has received 81 citations till now. The article focuses on the topics: Strongly connected component & Modular decomposition.read more
Figures
Fig. 4. Example graph being trimmed in (a) by forward and backward trims. Part (b) shows the predecessor, descendant, and remainder markings of the resulting dark shadow for the selected pivot (the solid vertex). Parts (c) and (d) show the subgraphs as they are reduced to strongly connected components. 
Fig. 5. Two grids used for testing the strongly connected component detection: (a) a rectangular mesh where the corner point of each cell is displaced by a random amount; (b) a hollow cylinder with the grid twisted along the vertical axis. 
Fig. 6. Effects of TRIM on execution time of ModifiedDCSC. 
Fig. 1. (a) An unstructured finite-element mesh (left) and its associated acyclic dependence graph for the angle shown (right). (b) A twisted ring of mesh elements that induces a cycle for the shown angle (left), and its dependence graph for the angle shown (right). A sweeping method will deadlock when it encounters a cycle such as this. 
Fig. 8. Measured speedup on an unscaled rectangular mesh on ASCI Red. Speedup is superlinear to 16 processors due to cache effects and falls off after 128 processors because there is very little work per processor. 
Fig. 7. Effects of mesh deformation on SCC count (a), and execution time, (b).
Citations
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Proceedings ArticleDOI
Computing Strongly Connected Components in Parallel on CUDA
TL;DR: This paper designs a new CUDA-aware procedure for pivot selection and adapt selected parallel algorithms for CUDA accelerated computation and experimentally demonstrates that with a single GTX 480 GPU card, this paper can easily outperform the optimal serial CPU implementation by an order of magnitude.
Proceedings ArticleDOI
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
TL;DR: It is shown that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes.
Proceedings ArticleDOI
On fast parallel detection of strongly connected components (SCC) in small-world graphs
TL;DR: This paper investigates the shortcomings of the conventional approach in parallel SCC detection and proposes a series of extensions that consider the fundamental properties of real-world graphs, e.g. the small-world property.
Proceedings ArticleDOI
BFS and Coloring-Based Parallel Algorithms for Strongly Connected Components and Related Problems
TL;DR: The Multistep method is introduced, a new approach that avoids work inefficiencies seen in prior SCC approaches and scales well on several real-world graphs, with performance fairly independent of topological properties such as the size of the largest SCC and the total number of SCCs.
Proceedings ArticleDOI
Distributed Memory Breadth-First Search Revisited: Enabling Bottom-Up Search
TL;DR: This work presents a scalable distributed-memory parallelization of this challenging BFS algorithm and achieves a performance rate of over 240 billion edges per second on 115 thousand cores of a Cray XE6, which makes it over 7× faster than a conventional top-down algorithm using the same set of optimizations and data distribution.
References
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Journal ArticleDOI
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.
Book ChapterDOI
Parallel algorithms for shared-memory machines
TL;DR: In this paper, the authors discuss parallel algorithms for shared-memory machines and discuss the theoretical foundations of parallel algorithms and parallel architectures, and present a theoretical analysis of the appropriate logical organization of a massively parallel computer.
ReportDOI
The Chaco user`s guide. Version 1.0
B. Hendrickson,R. Leland +1 more
TL;DR: The Chaco software package allows for recursive application of any of several different methods for finding small edge separators in weighted graphs, including inertial, spectral, Kernighan-Lin and multilevel methods in addition to several simpler strategies.
Journal ArticleDOI
Depth-first search is inherently sequential
TL;DR: It is shown that this problem, for undirected and directed graphs, is complete in deterministic polynomial time with respect to deterministic log-space reductions.
Book
Faster optimal parallel prefix sums and list ranking
Richard Cole,Uzi Vishkin +1 more
TL;DR: A parallel algorithm for the prefix sums problem which runs in timeO( logn/log logn) time using n/lognprocessors (optimal speedup) is presented.