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 …

We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up
to polylogarithmic factors in five models of computation: the two-party communication, AND …

We study the complexity of determining the edge connectivity of a simple graph with cut
queries. We show that (i) there is a bounded-error randomized algorithm that computes …

We devise new cut sparsifiers that are related to the classical sparsification of Nagamochi
and Ibaraki [Algorithmica, 1992], which is an algorithm that, given an unweighted graph G on …

We introduce the notion of fair cuts as an approach to leverage approximate (s, t)-mincut
(equivalently (s, t)-maxflow) algorithms in undirected graphs to obtain near-linear time …

In this paper we describe a randomized algorithm which returns a maximal spanning forest
of an unknown {\em weighted} undirected graph making $ O (n) $$\mathsf {CUT} $ queries …

A cactus representation of a graph, introduced by Dinitz et al. in 1976, is an edge sparsifier
of O (n) size that exactly captures all global minimum cuts of the graph. It is a central …

The hypergraph unreliability problem asks for the probability that a hypergraph gets
disconnected when every hyperedge fails independently with a given probability. For …

Given an undirected, weighted $ n $-vertex graph $ G=(V, E, w) $, a Gomory-Hu tree $ T $ is
a weighted tree on $ V $ such that for any pair of distinct vertices $ s, t\in V $, the Min-$ s …