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On κ-partitioning the n-cube

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Graph-Theoretic Concepts in Computer Science (WG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1197))

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Abstract

Let an edge cut partition the vertex set of the n-cube into κ subsets A 1,..., A k with ∥A i¦ — ¦Aj∥ ⩽ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form κ=2a±2b with a≥b≥0.

This work was partially supported by the German Research Association (DFG) within the project SFB 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen”.

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References

  1. Chung P.R.K., Yao S.-T.: A Near Optimal Algorithm for Edge Separators. In: Proc. 26th Symp. Theory of Comp. ACM, 1994.

    Google Scholar 

  2. Schwabe E.J.: Optimality of a VLSI Decomposition Scheme for the De-Bruijn Graph. Parallel Process. Lett., 3 (1993) 261–265.

    Google Scholar 

  3. Cypher R.: Theoretical Aspects of VLSI Pin Limitations. SIAM J. Comput., 22 (1993) 356–378.

    Google Scholar 

  4. Diekmann R., Lüling R., Monien B., Spräner C.: Combining Helpful Sets and Parallel Simulated Annealing for the Graph-Partitioning Problem. Int. J. Parallel Algorithms and Applications, (to appear).

    Google Scholar 

  5. Diekmann R., Meyer D., Monien B.: Parallel Decomposition of Unstructured FEM-Meshes. In: Proc. of IRREGULAR'95, Springer LNCS 980 (1995) 199–215.

    Google Scholar 

  6. Gilbert J.R., Miller G.L., Teng S.-H.: Geometric Mesh Partitioning: Implementation and Experiments. In: Proc. of IPPS'95, 1995.

    Google Scholar 

  7. Harper L.H.: Optimal assignment of numbers to vertices. J. Soc. Ind. Appl. Math., 12 (1964) 131–135.

    Google Scholar 

  8. Lipton R.J., Tarjan R.E.: A Separator Theorem for Planar Graphs. SIAM J. Appl. Math., 36 (1979) 177–189.

    Google Scholar 

  9. Rolim J., Sýkora O., Vrt'o I.: Optimal Cutwidth and Bisection Width of 2-and 3-Dimensional Meshes. In: Proc. of WG'95, 1995.

    Google Scholar 

  10. Seitz C.: The Cosmic Cube. Comm ACM, 28 (1985) 22–33.

    Google Scholar 

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Authors and Affiliations

  1. Department of Math. and Comp. Sci., University of Paderborn, D-33095, Paderborn, Germany

    Sergej L. Bezrukov

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  1. Sergej L. Bezrukov
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Fabrizio d'Amore Paolo Giulio Franciosa Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Bezrukov, S.L. (1997). On κ-partitioning the n-cube. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_5

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  • DOI: https://doi.org/10.1007/3-540-62559-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62559-9

  • Online ISBN: 978-3-540-68072-7

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