Year: 2021
Type: conference-paper
Abstract: The Gomory-Hu tree or cut tree (Gomory and Hu, 1961) is a classic data structure for reporting s−t mincuts (and by duality, the values of s−t maxflows) for all pairs of vertices s and t in an undirected graph. Gomory and Hu showed that it can be computed using n−1 exact maxflow computations. Surprisingly, this remains the best algorithm for Gomory-Hu trees more than 50 years later, even for approximate mincuts. In this paper, we break this longstanding barrier and give an algorithm for computing a (1+є)-approximate Gomory-Hu tree using log(n) maxflow computations. Specifically, we obtain the runtime bounds we describe below.
Authors: Jason Li, Debmalya Panigrahi
Institutions: Carnegie Mellon University, Duke University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
Awards: Collaborative Research: AF: Small: Combinatorial Optimization for Stochastic Inputs, Collaborative Research: AF: Medium: Algorithms Meet Machine Learning: Mitigating Uncertainty in Optimization, AF: Small: New Approaches for Approximation and Online Algorithms, CAREER: New Directions in Graph Algorithms, Collaborative Research: AF: Medium: Algorithms Meet Machine Learning: Mitigating Uncertainty in Optimization
OpenAlex ID: W3170659189