Parallel Algorithm for Finding the Minimum Edges to Make a Disconnected Directed Acyclic Graph Strongly Connected

Itokawa, Tsuyoshi; Tada, Akio; Migita, Masahiro

doi:10.1109/icicic.2007.437

Cited by 1 publication

(3 citation statements)

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“…It follows that there cannot be a edge (10,14), for otherwise the level of node 14 in the BFS-tree must be 3, 4, or 5. A similar argument can be made for the edge (12,14) and hence the graph induced by those vertices is not connected. From the above reasoning it is evident that using the graph's BFS-tree can be an effective tool in reducing the number of combinations to be tested.…”

Section: Using Bfs-tree Information To Reduce the Number Of Computatimentioning

confidence: 92%

“…Also, representing the edge information using arrays to store the out-vertex and in-vertex numbers saves space for sparse matrices [12]. This method is better suited for directed graphs.…”

Section: Related Workmentioning

confidence: 99%

“…It is possible for nodes 10 and 12 to be connected by an edge since they are in adjacent levels. For the sake of discussion, assume there is an edge (10,12) in the graph. It follows that there cannot be a edge (10,14), for otherwise the level of node 14 in the BFS-tree must be 3, 4, or 5.…”

Section: Using Bfs-tree Information To Reduce the Number Of Computatimentioning

confidence: 99%

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Data Structures and Algorithms for Counting Problems on Graphs using GPU

Chatterjee

Radhakrishnan

Antonio

2013

IJNC

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The availability and utility of large numbers of Graphical Processing Units (GPUs) have enabled parallel computations using extensive multi-threading. Sequential access to global memory and contention at the size-limited shared memory have been main impediments to fully exploiting potential performance in architectures having a massive number of GPUs. After performing extensive study of data structures and complexity analysis of various data access methodologies, we propose novel memory storage and retrieval techniques that enable parallel graph computations to overcome the above issues. More specifically, given a graph G = (V, E) and an integer k <= |V |, we provide both storage techniques and algorithms to count the number of: a) connected subgraphs of size k; b) k cliques; and c) k independent sets, all of which can be exponential in number. Our storage techniques are based on creating a breadth-first search tree and storing it along with non-tree edges in a novel way. Our experiments solve the above mentioned problems by using both naïve and advanced data structures on the CPU and GPU. Speedup is achieved by solving the problems on the GPU even using a brute-force approach as compared to the implementations on the CPU. Utilizing the knowledge of BFS-tree properties, the performance gain on the GPU increases and ultimately outperforms the CPU by a factor of at least 5 for graphs that completely fit in the shared memory and by a factor of 10 for larger graphs stored using the global memory. The counting problems mentioned above have many uses, including the analysis of social networks.

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Section: Using Bfs-tree Information To Reduce the Number Of Computatimentioning

confidence: 92%

“…Also, representing the edge information using arrays to store the out-vertex and in-vertex numbers saves space for sparse matrices [12]. This method is better suited for directed graphs.…”

Section: Related Workmentioning

confidence: 99%