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Scalable Sparse Topologies with Small Spectrum

  • Robert Elsässer
  • Rastislav Královič
  • Burkhard Monien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

One of the fundamental properties of a graph is the number of distinct eigenvalues of its adjacency or Laplacian matrix. Determining this number is of theoretical interest and also of practical impact. Graphs with small spectra exhibit many symmetry properties and are well suited as interconnection topologies. Es- pecially load balancing can be done on such interconnection topologies in a small number of steps. In this paper we are interested in graphs with maximal degree O(log n), where n is the number of vertices, and with a small number of distinct eigenvalues. Our goal is to find scalable families of such graphs with polyloga- rithmic spectrum in the number of vertices. We present also the eigenvalues of the Butterfly graph.

Keywords

Load Balance Adjacency Matrix Maximal Degree Laplacian Matrix Vertex Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Robert Elsässer
    • 1
  • Rastislav Královič
    • 2
  • Burkhard Monien
    • 1
  1. 1.University of PaderbornGermany
  2. 2.Comenius UniversityMFF-UK BratislavaSlovakia

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