A sublinear time quantum algorithm for s-t minimum cut on dense simple graphs
share
An s-t minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices s and t. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from s to t. In this work we describe a quantum algorithm for the minimum s-t cut problem on undirected graphs. For an undirected graph with n vertices, m edges, and integral edge weights bounded by W, the algorithm computes with high probability the weight of a minimum s-t cut in time O(√(m) n^5/6 W^1/3 + n^5/3 W^2/3), given adjacency list access to G. For simple graphs this bound is always O(n^11/6), even in the dense case when m = Ω(n^2). In contrast, a randomized algorithm must make Ω(m) queries to the adjacency list of a simple graph G even to decide whether s and t are connected.
READ FULL TEXT