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ECCC
2000

On Testing Expansion in Bounded-Degree Graphs

8 years 3 months ago
On Testing Expansion in Bounded-Degree Graphs
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 < 1, oracle access to a bounded-degree N-vertex graph, and two additional parameters , > 0. The algorithm runs in time N0.5+ /poly(), and accepts any graph having (normalized) second eigenvalue at most . We believe that the algorithm rejects any graph that is -far from having second eigenvalue at most /O(1) , and prove the validity of this belief under an appealing combinatorial conjecture.
Oded Goldreich, Dana Ron
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where ECCC
Authors Oded Goldreich, Dana Ron
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