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Parallel computing of fragment vector in Steiner triple systems

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Vector and Parallel Processing — VECPAR'96 (VECPAR 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1215))

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Abstract

In this paper we describe a linear time algorithm using O(n 2) processors for computing the fragment vector in Steiner triple systems. The algorithm is designed for SIMD machine having a grid interconnection network. We show the implementation and some experimental results obtained on the Connection Machine CM-2.

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References

  1. Brouwer, A. E.: Steiuer triple systems without forbidden subconfigurations. Math. Centrum Amsterdam, ZW 104/77.

    Google Scholar 

  2. Brown, W. G., Erdös, P., Sos, V. T.: Some extremal problems on r-graphs. New directions in the theory of graphs, Acad. Press NY (1973) 53–63

    Google Scholar 

  3. Gibbons, P. D.: Computing techniques for the construction and analysis of block designs. Ph.D. Thesis, University of Toronto (1976)

    Google Scholar 

  4. Grannell, M. J., Griggs, T. S., Mendelsohn, E.: A small basis for four-line configurations in Steiner triple systems. Journal of Combinatorial Designs, Vol. 3, 1 (1995) 51–59

    Google Scholar 

  5. Griggs, T. S., Mendelsohn, E., Rosa, A.: Simultaneous decomposition of Steiner triple systems. Ars Combinatoria 37 (1994) 157–173

    Google Scholar 

  6. Griggs, T. S., de Resmini, M. J., Rosa, A.: Decomposing Steiner triple systems into four-line configurations. Annals of Discrete Math. 52 (1992) 215–226

    Google Scholar 

  7. Griggs, T. S., Murphy, J. P., Phelan, J. S.: Anti-Pasch Steiner triple systems. J. Combin. Inform. System Sci. 15 (1990) 79–84

    Google Scholar 

  8. S. Horak, P., Phillips, N., Wallis, W. D., Yucas, J.: Counting frequencies of configurations in Steiner triple systems. Journal of Combinatorial Designs (to appear)

    Google Scholar 

  9. Horak, P., Rosa, A.: Decomposing Steiner triple systems into small configurations. Ars Combinatoria 26 (1988) 91–105

    Google Scholar 

  10. Kirkman, T. P.: On a. problem in combinations. Cambridge and Dublin Mathematical Journal (1847) 191–204

    Google Scholar 

  11. Mathon, R. A., Phelps, K. T., Rosa, A.: Small Steiner systems and their properties. Ars Combinatoria 15 (1983) 3–110

    Google Scholar 

  12. Stinson, D. R.: Hill-climbing algorithms for the construction of combinatorial designs. Annals of Discrete Math. 26 (1985), 321–334

    Google Scholar 

  13. Stinson, D. R., Wei, Y. J.: Some results on quadrilaterals in Steiner triple systems. Discrete Math. 105 (1992) 207–219

    Google Scholar 

  14. Urland, E.: A linear basis for the 7-line configurations. Journal of Comb. Math. and Comb. Computing (to appear)

    Google Scholar 

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José M. L. M. Palma Jack Dongarra

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© 1997 Springer-Verlag Berlin Heidelberg

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Urland, E. (1997). Parallel computing of fragment vector in Steiner triple systems. In: Palma, J.M.L.M., Dongarra, J. (eds) Vector and Parallel Processing — VECPAR'96. VECPAR 1996. Lecture Notes in Computer Science, vol 1215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62828-2_128

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  • DOI: https://doi.org/10.1007/3-540-62828-2_128

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62828-6

  • Online ISBN: 978-3-540-68699-6

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