DeepAI
Log In Sign Up

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

10/17/2019
by   Julia Chuzhoy, et al.
0

We consider the classical Minimum Balanced Cut problem: given a graph G, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first deterministic, almost-linear time approximation algorithm for this problem. Our algorithm in fact 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. We use this algorithm to obtain deterministic algorithms for dynamic connectivity and minimum spanning forest, whose worse-case update time on an n-vertex graph is n^o(1), thus resolving a major open problem in the area of dynamic graph algorithms. Our work also implies deterministic algorithms for a host of additional problems, whose time complexities match, up to subpolynomial in n factors, those of known randomized algorithms. The implications include almost-linear time deterministic algorithms for solving Laplacian systems and for approximating maximum flows in undirected graphs.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/25/2022

Deterministic Small Vertex Connectivity in Almost Linear Time

In the vertex connectivity problem, given an undirected n-vertex m-edge ...
11/02/2021

Finding the KT partition of a weighted graph in near-linear time

In a breakthrough work, Kawarabayashi and Thorup (J. ACM'19) gave a near...
11/17/2019

Quantum Speedup for Graph Sparsification, Cut Approximation and Laplacian Solving

Graph sparsification underlies a large number of algorithms, ranging fro...
09/19/2022

A Simple Framework for Finding Balanced Sparse Cuts via APSP

We present a very simple and intuitive algorithm to find balanced sparse...
10/17/2019

Deterministic Graph Cuts in Subquadratic Time: Sparse, Balanced, and k-Vertex

We study deterministic algorithms for computing graph cuts, with focus o...
08/15/2017

Derandomization Beyond Connectivity: Undirected Laplacian Systems in Nearly Logarithmic Space

We give a deterministic Õ( n)-space algorithm for approximately solving ...