Sparsest cuts and bottlenecks in graphs (Q810053)

It is shown that the problem of finding a sparsest cut of a graph is NP- hard in general. However, certain classes of graphs on n vertices are shown to admit solutions in O(n), \(O(n^ 2)\) and \(O(n^ 2\sqrt{\log n})\) times respectively. The paper goes on to consider the maximum concurrent flow problem. In this problem, cuts with maximum density are termed ``bottle necks''. The near dual relationship between this problem and the sparsest cut problem is exploited to determine a broad class of graphs for which the sparsest cut problem is efficiently solvable.