Abstract
Algorithms are considered for the external connected-components problem. The main contribution is an algorithm which for a graph with n nodes and m edges has an expected running time bounded by O(m · loglog n) when randomizing the node indices. A blocked version of this algorithm, which is perfectly suited for external application, handles bundles of W nodes at a time. For random graphs, the running time of this algorithm is bounded by O(loglog (n 2 / (m · W)) · m). A special case of the algorithm solves the list-ranking and tree-rooting problem. The running time of this algorithm is linear in the number of involved nodes, independently of their arrangement.
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References
Abello, J., Buchsbaum, A.L., Westbrook, J.R.: A Functional Approach to External Graph Algorithms. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 332–343. Springer, Heidelberg (1998) ;Full version AT & T Research Report ,TR 99.1.1 (1999)
Anderson, R.J., Miller, G.L.: Deterministic Parallel List Ranking. Algorithmica 6, 859–868 (1991)
Arge, L., Brodal, G., Toma, L.: On External Memory MST, SSSP and Multi-Way Planar Graph Separation. In: Halldórsson, M.M. (ed.) SWAT 2000. LNCS, vol. 1851, pp. 433–447. Springer, Heidelberg (2000)
Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-Memory Graph Algorithms. In: Proc. 6th Symposium on Discrete Algorithms, pp. 139–149. ACM-SIAM (1995)
Chin, F.Y., Lam, J., Chen, I.: ‘Efficient Parallel Algorithms for some Graph Problems,’. Communications of the ACM 25(9), 659–665 (1982)
Crauser, A., Mehlhorn, K.: Lecture notes on algorithms for very large data sets (1997) , http://www.mpi-sb.mpg.de/~crauser/courses.html
Hirschberg, D.S., Chandra, A.K., Sarwate, D.V.: ‘Computing Connected Components on Parallel Computers,’. Communications of the ACM 22(8), 461–464 (1979)
Karger, D.R., Klein, P.N., Tarjan, R.E.: A randomized linear-time algorithm to find minimum spanning trees. Journal of the ACM 42(2), 321–328 (1995)
Meyer, U., Sanders, P., Sibeyn, J.F. (eds.): Algorithms for Memory Hierarchies. LNCS, vol. 2625. Springer, Heidelberg (2003)
Munagala, K., Ranade, A.: I/O-Complexity of Graph Algorithms. In: 10th Symposium on Discrete Algorithms, pp. 687–694. ACM-SIAM (1999)
Sibeyn, J.F.: Ultimate Parallel List Ranking? In: Proc. 6th Conference on High Performance Computing. LNCS, Springer, Heidelberg (1999) ;Full version Techn. Rep. MPII- 99-1005, Max-Planck-Institut für Informatik, Saarbrücken, Germany (1999)
Vitter, J.S.: External Memory Algorithms and Data Structures: Dealing with Massive Data. ACM Computing Surveys 33(2), 209–271 (2001)
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Sibeyn, J.F. (2004). External Connected Components. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_40
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DOI: https://doi.org/10.1007/978-3-540-27810-8_40
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