@inproceedings{Raghavendra2010GraphEA,
title={Graph expansion and the unique games conjecture},
author={Prasad Raghavendra and David Steurer},
booktitle={STOC},
year={2010}
}

The edge expansion of a subset of vertices S ⊆ V in a graph G measures the fraction of edges that leave S. In a d-regular graph, the edge expansion/conductance Φ(S) of a subset S ⊆ V is defined as Φ(S) = (|E(S, V\S)|)/(d|S|). Approximating the conductance of small linear sized sets (size δ n) is a natural optimization question that is a variant of the well-studied Sparsest Cut problem. However, there are no known algorithms to even distinguish between almost complete edge expansion (Φ(S) = 1… CONTINUE READING