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On Euclidean Embeddings and Bandwidth Minimization

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Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques (RANDOM 2001, APPROX 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2129))

Abstract

We study Euclidean embeddings of Euclidean metrics and present the following four results: (1) an O(log3 n√log log n) approximation for minimum bandwidth in conjunction with a semi-definite relaxation, (2) an O(log3 n) approximation in O(n log n) time using a new constraint set, (3) a lower bound of Θ(√log n) on the least possible volume distortion for Euclidean metrics, (4) a new embedding with O(√log n) distortion of point-to-subset distances.

Supported in part by NSF Career Award CCR-9875024.

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References

  1. A. Blum, G. Konjevod, R. Ravi, and S. Vempala, “Semi-Definite Relaxations for Minimum Bandwidth and other Vertex-Ordering Problems,” Proc. 30th ACM Symposium on the Theory of Computing, 1998.

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Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139

    John Dunagan & Santosh Vempala

Authors
  1. John Dunagan
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  2. Santosh Vempala
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, MIT, Cambridge, MA, 02139, USA

    Michel Goemans

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, Université de Genéve, 24, Rue General Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  4. Computer Science Division, University of California at Berkeley, 615 Soda Hall, Berkeley, CA, 94720-1776, USA

    Luca Trevisan

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© 2001 Springer-Verlag Berlin Heidelberg

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Dunagan, J., Vempala, S. (2001). On Euclidean Embeddings and Bandwidth Minimization. In: Goemans, M., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques. RANDOM APPROX 2001 2001. Lecture Notes in Computer Science, vol 2129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44666-4_26

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  • DOI: https://doi.org/10.1007/3-540-44666-4_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42470-3

  • Online ISBN: 978-3-540-44666-8

  • eBook Packages: Springer Book Archive

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