Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues

Authors Gary L. Miller, Noel J. Walkington, Alex L. Wang



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Author Details

Gary L. Miller
  • Carnegie Mellon University, Pittsburgh, PA, USA
Noel J. Walkington
  • Carnegie Mellon University, Pittsburgh, PA, USA
Alex L. Wang
  • Carnegie Mellon University, Pittsburgh, PA, USA

Acknowledgements

We would like to thank Timothy Chu for many helpful discussions.

Cite AsGet BibTex

Gary L. Miller, Noel J. Walkington, and Alex L. Wang. Hardy-Muckenhoupt Bounds for Laplacian Eigenvalues. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.8

Abstract

We present two graph quantities Psi(G,S) and Psi_2(G) which give constant factor estimates to the Dirichlet and Neumann eigenvalues, lambda(G,S) and lambda_2(G), respectively. Our techniques make use of a discrete Hardy-type inequality due to Muckenhoupt.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Spectra of graphs
  • Mathematics of computing → Approximation algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Hardy
  • Muckenhoupt
  • Laplacian
  • eigenvalue
  • effective resistance

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