Abstract
The Union-Find algorithm is used for maintaining a number of non-overlapping sets from a finite universe of elements. The algorithm has applications in a number of areas including the computation of spanning trees, sparse linear algebra, and in image processing.
Although the algorithm is inherently sequential there has been some previous efforts at constructing parallel implementations. These have mainly focused on shared memory computers. In this paper we present the first scalable parallel implementation of the Union-Find algorithm suitable for distributed memory computers. Our new parallel algorithm is based on an observation of how the Find part of the sequential algorithm can be executed more efficiently.
We show the efficiency of our implementation through a series of tests to compute spanning forests of very large graphs.
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References
Anderson, R.J., Woll, H.: Wait-free parallel algorithms for the union-find problem. In: Proceedings of The Twenty-Third Annual ACM Symposium on Theory of Computing (STOC 1991), pp. 370–380 (1991)
Bader, D.A., Madduri, K.: GTGraph: A synthetic graph generator suite (2006), http://www.cc.gatech.edu/~kamesh/GTgraph
Bader, D.J., Cong, G.: A fast, parallel spanning tree algorithm for symmetric multiprocessors (smps). Journal of Parallel and Distributed Computing 65, 994–1006 (2005)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press, Cambridge (2001)
Cybenko, G., Allen, T.G., Polito, J.E.: Practical parallel algorithms for transitive closure and clustering. International Journal of Parallel Computing 17, 403–423 (1988)
Davis, T.A.: University of Florida sparse matrix collection. ACM Transactions on Mathematical Software (submitted)
Gebremedhin, A.H., Tarafdar, A., Manne, F., Pothen, A.: New acyclic and star coloring algorithms with applications to computing hessians. SIAM Journal on Scientific Computing 29, 515–535 (2007)
Koster, J.: Parasol matrices, http://www.parallab.uib.no/projects/parasol/data
Tarjan, R.E., van Leeuwen, J.: Worst-case analysis of set union algorithms. J. ACM 31, 245–281 (1984)
Vastenhouw, B., Bisseling, R.H.: A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Review 47, 67–95 (2005)
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Manne, F., Patwary, M.M.A. (2010). A Scalable Parallel Union-Find Algorithm for Distributed Memory Computers. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_20
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DOI: https://doi.org/10.1007/978-3-642-14390-8_20
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