On testing expansion in bounded-degree graphs

Oded Goldreich; Dana Ron

doi:10.1007/978-3-642-22670-0_9

On testing expansion in bounded-degree graphs

Oded Goldreich, Dana Ron

Weizmann Institute of Science, Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We consider testing graph expansion in the bounded-degree graph model. Specifically, we refer to algorithms for testing whether the graph has a second eigenvalue bounded above by a given threshold or is far from any graph with such (or related) property. We present a natural algorithm aimed towards achieving the foregoing task. The algorithm is given a (normalized) eigenvalue bound λ < 1, oracle access to a bounded-degree N-vertex graph, and two additional parameters ε,α > 0. The algorithm runs in time N ^0.5+α /poly(ε), and accepts any graph having (normalized) second eigenvalue at most λ. We believe that the algorithm rejects any graph that is ε-far from having second eigenvalue at most λ ^α/O(1), and prove the validity of this belief under an appealing combinatorial conjecture.

Original language	English
Title of host publication	Studies in Complexity and Cryptography
Subtitle of host publication	Miscellanea on the Interplay between Randomness and Computation
Editors	Oded Goldreich
Chapter	9
Pages	68-75
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-642-22670-0_9
State	Published - 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6650 LNCS

Keywords

Graph Expansion
Property Testing

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-22670-0_9

Cite this

Goldreich, O., & Ron, D. (2011). On testing expansion in bounded-degree graphs. In O. Goldreich (Ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation (pp. 68-75). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS). https://doi.org/10.1007/978-3-642-22670-0_9

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Goldreich, O & Ron, D 2011, On testing expansion in bounded-degree graphs. in O Goldreich (ed.), Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6650 LNCS, pp. 68-75. https://doi.org/10.1007/978-3-642-22670-0_9

On testing expansion in bounded-degree graphs. / Goldreich, Oded; Ron, Dana.
Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. ed. / Oded Goldreich. 2011. p. 68-75 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6650 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AB - We consider testing graph expansion in the bounded-degree graph model. Specifically, we refer to algorithms for testing whether the graph has a second eigenvalue bounded above by a given threshold or is far from any graph with such (or related) property. We present a natural algorithm aimed towards achieving the foregoing task. The algorithm is given a (normalized) eigenvalue bound λ < 1, oracle access to a bounded-degree N-vertex graph, and two additional parameters ε,α > 0. The algorithm runs in time N 0.5+α /poly(ε), and accepts any graph having (normalized) second eigenvalue at most λ. We believe that the algorithm rejects any graph that is ε-far from having second eigenvalue at most λ α/O(1), and prove the validity of this belief under an appealing combinatorial conjecture.

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Goldreich O, Ron D. On testing expansion in bounded-degree graphs. In Goldreich O, editor, Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation. 2011. p. 68-75. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22670-0_9

On testing expansion in bounded-degree graphs

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