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Vectorized search for single clusters

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Abstract

Breadth-first search for a single cluster on a regular lattice is shown to be vectorizable. It is applied to construct clusters in the single-cluster variant of the Swendsen-Wang algorithm. On a Cray-YMP, total CPU time has been reduced by factors of 3.5–7 in large-scale applications. A multiple-cluster version is also described.

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References

  1. T. H. Cormen, C. E. Leiserson, and R. L. Rivest,Introduction to Algorithms (MIT Press, Cambridge, Massachusetts, 1990).

    Google Scholar 

  2. R. H. Swendsen and J. S. Wang,Phys. Rev. Lett. 58:86 (1987).

    Google Scholar 

  3. U. Wolff, Collective Monte Carlo updating for spin systems,Phys. Rev. Lett. 62:361 (1989); see also P. L. Leigh, Cluster size and boundary distribution near percolation threshold,Phys. Rev. B 14:5046 (1976).

    Google Scholar 

  4. U. Wolff, Critical slowing down, in Lattice '89, Capri 1989, N. Cabbiboet al., eds.,Nucl. Phys. B (Proc. Suppl.) 17:93 (1990); A. D. Sokal, How to beat critical slowing down: 1990 update, in Lattice '90, Tallahassee 1990, U. M. Helleret al., eds.,Nucl Phys. B (Proc. Suppl.) 20:55 (1991).

  5. Y. Shiloach and U. Vishkin, AnO(logn) parallel connectivity algorithm,J. Algorithms 3:57 (1982).

    Google Scholar 

  6. J. L. C. Sanz and R. Cypher, Data reduction and fast routing: A strategy for efficient algorithms for message-passing parallel computers,Algorithmica 7:77 (1992).

    Google Scholar 

  7. R. C. Brower, P. Tamayo, and B. York, A parallel multigrid algorithm for percolation clusters,J. Stat. Phys. 63:73 (1991); J. Apostolakis, P. Coddington, and E. Marinari, A multi-grid cluster labeling scheme,Europhys. Lett. 17:189 (1992); P. Rossi, and G. P. Tecchiolli, Finding clusters in a parallel environment, preprint, (October 1991); H. Mino, A vectorized algorithm for cluster formation in the Swendsen-Wang dynamics,Computer Phys. Commun. 66:25 (1991).

    Google Scholar 

  8. R. G. Edwards and A. D. Sokal, Sequential and vectorized algorithms for computing the connected components of an undirected graph, in preparation.

  9. C. F. Baillie and P. D. Coddington, Cluster identification algorithms for spin models — Sequential and parallel,Concurrency: Practice Experience 3:129 (1991).

    Google Scholar 

  10. H. G. Evertz, M. Hasenbusch, M. Marcu, K. Pinn, and S. Solomon, Stochastic cluster algorithms for discrete gaussian (SOS) models,Phys. Lett. B 254:185 (1991); High precision measurement of the SOS surface thickness in the rough phase,J. Phys. J 1:1669 (1991).

    Google Scholar 

  11. H. G. Evertz, R. Ben-Av, M. Marcu, and S. Solomon, Critical acceleration of finite temperatureSU(2) gauge simulations,Phys. Rev. D 44:2953 (1991).

    Google Scholar 

  12. M. Klomfass, private communication.

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Evertz, H.G. Vectorized search for single clusters. J Stat Phys 70, 1075–1079 (1993). https://doi.org/10.1007/BF01053610

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  • DOI: https://doi.org/10.1007/BF01053610

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