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


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

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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)


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
  • Hardy
  • Muckenhoupt
  • Laplacian
  • eigenvalue
  • effective resistance


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