scholarly journals A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest

1999 ◽  
pp. 233-244 ◽  
Author(s):  
Seth Pettie ◽  
Vijaya Ramachandran
Keyword(s):  
Parallel Algorithm ◽  
Spanning Forest ◽  
Time Work ◽  
Minimum Spanning Forest

scholarly journals ConnectIt

2020 ◽  
Vol 14 (4) ◽  
pp. 653-667
Author(s):  
Laxman Dhulipala ◽  
Changwan Hong ◽  
Julian Shun
Keyword(s):  
Experimental Evaluation ◽  
Comprehensive Evaluation ◽  
State Of The Art ◽  
Graph Connectivity ◽  
Connected Components ◽  
Sampling Strategies ◽  
Spanning Forest ◽  
Speed Up ◽  
Minimum Spanning Forest ◽  
Edge Sampling

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

Some statistical properties of the minimum spanning forest

1983 ◽  
Vol 16 (5) ◽  
pp. 525-531 ◽  
Author(s):  
V. Di Gesù ◽  
B. Sacco
Keyword(s):  
Statistical Properties ◽  
Spanning Forest ◽  
Minimum Spanning Forest
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