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From expanders to better superconcentrators without cascading

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STACS 84 (STACS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 166))

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Abstract

Superconcentration is a strong property of interconnection diagraphs. We characterize its negation by existence of two disjoint and seperated sets which shrink under the forward and backward neighbor relation, respectively. This enables a better, non-cascaded design of superconcentrators, explicit ones with edge density ≤ 118, random ones with edge density ≤ 13.

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References

  1. L.A. Bassalygo, Asymptotically optimal swiching circuits. Problems of Information Transmission (1981), 206–211. [in Russian].

    Google Scholar 

  2. O. Gabber and Z. Galil, Explicit construction of linear size superconcentrators. Proc. of IEEE 20th FOCS Conference 1971, 364–370.

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  3. G.R. Grimmett and H. Kesten, First — passage perculation, network flows and electrical resistances 1982 (to appear).

    Google Scholar 

  4. G. A. Margulis, Explicit construction of concentrators. Problems of Information Transmissiom 9 (1973), 71–80 [in Russian, English translation plenum 1975]

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  5. E. Shamir and E. Upfal, 1 — factor in random graphs based on vertex choice. Discrete Math. 41 (1982), 281–286.

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  6. E. Shamir and E. Upfal, On factors in random graphs. Israel J. of Math. 39 (1981), 296–301.

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M. Fontet K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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Shamir, E. (1984). From expanders to better superconcentrators without cascading. In: Fontet, M., Mehlhorn, K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12920-0_11

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  • DOI: https://doi.org/10.1007/3-540-12920-0_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12920-2

  • Online ISBN: 978-3-540-38805-0

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