Quantum Algorithms for Matching and Network Flows
Abstract
We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrtm+n log n), finding a maximal non-bipartite matching in time O(n2 (sqrtm/n + log n) log n), and finding a maximal flow in an integer network in time O(min(n7/6 sqrt m * U1/3, sqrtn U m) log n), where n is the number of vertices, m is the number of edges, and U <= n1/4 is an upper bound on the capacity of an edge.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.