期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2000
卷号：2000
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：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 above
task. The algorithm is given a (normalized) second eigenvalue
bound 1, oracle access to a bounded-degree N-vertex graph,
and two additional parameters 0 .
The algorithm runs in time N05+\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.
