• Corpus ID: 233289657

Minimum Cuts in Directed Graphs via $\sqrt{n}$ Max-Flows

  title={Minimum Cuts in Directed Graphs via \$\sqrt\{n\}\$ Max-Flows},
  author={Ruoxu Cen and Jason Li and Danupon Nanongkai and Debmalya Panigrahi and Thatchaphol Saranurak},
We give an algorithm to find a mincut in an n-vertex, m-edge weighted directed graph using Õ( √ n) calls to any maxflow subroutine. Using state of the art maxflow algorithms, this yields a directed mincut algorithm that runs in Õ(m √ n+ n) time. This improves on the 30 year old bound of Õ(mn) obtained by Hao and Orlin for this problem. ar X iv :2 10 4. 07 89 8v 1 [ cs .D S] 1 6 A pr 2 02 1 

Figures from this paper



Deterministic mincut in almost-linear time

  • Jason Li
  • Computer Science, Mathematics
  • 2021
This work de-randomizes the construction of the skeleton graph in Karger’s near-linear time mincut algorithm, which is its only randomized component, and designs an efficient pessimistic estimator to capture the cuts of a graph, harnessing the expander decomposition framework introduced in recent work by Goranci et al.

Faster Algorithms for Rooted Connectivity in Directed Graphs

A new randomized Monte Carlo algorithm that runs in time Õ ( n ) .

Fast Approximations for Rooted Connectivity in Weighted Directed Graphs

This work considers approximations for computing minimum weighted cuts in directed graphs, and gives randomized Monte Carlo algorithms that compute a $(1+\epsilon)$-approximate minimum cut in $\tilde{O}(n^2 / \ep silon^2)$ time.

Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao

The algorithm revolves around dynamically maintaining the augmenting electrical flows at the core of the interior point method based algorithm from [Mądry JACM '16]. This entails designing data structures that, in limited settings, return edges with large electric energy in a graph undergoing resistance updates.

Minimum cost flows, MDPs, and ℓ1-regression in nearly linear time for dense instances

New randomized algorithms with improved runtimes for solving linear programs with two-sided constraints with dynamic data structures for efficiently maintaining approximations to variants of Lewis-weights, a fundamental importance measure for matrices which generalize leverage scores and effective resistances are provided.

A Deterministic Algorithm for Balanced Cut with Applications to Dynamic Connectivity, Flows, and Beyond

The first deterministic, almost-linear time approximation algorithm for the classical Minimum Balanced Cut problem, which provides a stronger guarantee: it either returns a balanced cut whose value is close to a given target value, or it certifies that such a cut does not exist by exhibiting a large subgraph of $G$ that has high conductance.

Network Flow and Testing Graph Connectivity

An algorithm of Dinic for finding the maximum flow in a network is described. It is then shown that if the vertex capacities are all equal to one, the algorithm requires at most $O(|V|^{1/2} \cdot

Efficient algorithms for finding minimum spanning trees in undirected and directed graphs

This paper uses F-heaps to obtain fast algorithms for finding minimum spanning trees in undirected and directed graphs and can be extended to allow a degree constraint at one vertex.

On edge-disjoint branchings

A simple direct proof of this lemma is given, thereby providing a simplerProof of Edmonds' theorem and a simpler proof that Tarjan's algorithm works.

Finding the Edge Connectivity of Directed Graphs