In a social network, nodes correspond topeople or other social entities, and edges
correspond to social links between them. In an effort to preserve privacy, the practice of …

Network flow theory has been used across a number of disciplines, including theoretical
computer science, operations research, and discrete math, to model not only problems in the …

Due to the lack of unconditional polynomial lower bounds, it is now in fashion to prove
conditional lower bounds in order to advance our understanding of the class P. The vast …

We give a deterministic (global) min-cut algorithm for weighted undirected graphs that runs
in time O (m 1+ ε) plus polylog (n) max-flow computations. Using the current best max-flow …

In 1961, Gomory and Hu showed that the All-Pairs Max-Flow problem of computing the max-
flow between all n\2 pairs of vertices in an undirected graph can be solved using only n-1 …

Every undirected graph G has a (weighted) cut-equivalent tree T, commonly named after
Gomory and Hu who discovered it in 1961. Both T and G have the same node set, and for …

We consider the problem of computing the rank of an m× n matrix A over a field. We present
a randomized algorithm to find a set of r= rank (A) linearly independent columns in Õ (| A|+ r …

In this article, we consider graph algorithms in models of computation where the space
usage (random accessible storage, in addition to the read-only input) is sublinear in the …

This article surveys the many facets of the Minimum Spanning Tree problem. We follow the
history of the problem since the first polynomial-time solution by Bor˚ uvka to the modern …

A Gomory-Hu tree (also called a cut tree) succinctly represents (s,t) min-cuts (and therefore,
(s,t) max-flow values) of all pairs of vertices s,t in an undirected graph. In this paper, we give …