Gomory-Hu Tree in Subcubic Time
share
In 1961, Gomory and Hu showed that the max-flow values of all n 2 pairs of vertices in an undirected graph can be computed using only n-1 calls to any max-flow algorithm, and succinctly represented them in a tree (called the Gomory-Hu tree later). Even assuming a linear-time max-flow algorithm, this yields a running time of O(mn) for this problem; with current max-flow algorithms, the running time is Õ(mn + n^5/2). We break this 60-year old barrier by giving an Õ(n^2)-time algorithm for the Gomory-Hu tree problem, already with current max-flow algorithms. For unweighted graphs, our techniques show equivalence (up to poly-logarithmic factors in running time) between Gomory-Hu tree (i.e., all-pairs max-flow values) and a single-pair max-flow.
READ FULL TEXT