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A Polynomial Regularity Lemma For Semialgebraic Hypergraphs And Its Applications In Geometry And Property Testing

Publications associées (56)

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Hypergraph-Based Fast Distributed AC Power Flow Optimization

Colin Neil Jones, Yuning Jiang, Yingzhao Lian, Xinliang Dai

This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...

New York2023

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Akash Kumar

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

IEEE COMPUTER SOC2022

On Semi-Algebraic Proofs and Algorithms

Mika Tapani Göös

We give a new characterization of the Sherali-Adams proof system, showing that there is a degree-d Sherali-Adams refutation of an unsatisfiable CNF formula C if and only if there is an ε > 0 and a degree-d conical junta J such that viol_C(x) - ε = J, where ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2022

A Toolbox for Barriers on Interactive Oracle Proofs

Alessandro Chiesa

Interactive oracle proofs (IOPs) are a proof system model that combines features of interactive proofs (IPs) and probabilistically checkable proofs (PCPs). IOPs have prominent applications in complexity theory and cryptography, most notably to constructing ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...

ASSOC COMPUTING MACHINERY2021

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut (MAXCUT) in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communica ...

ELSEVIER2020

Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples

Mikhail Kapralov, Slobodan Mitrovic, Ashkan Norouzi Fard, Jakab Tardos

Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...

ASSOC COMPUTING MACHINERY2020

New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

Local Approximation of the Maximum Cut in Regular Graphs

Etienne Michel François Bamas

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication and ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

An Optimal Space Lower Bound for Approximating MAX-CUT

Mikhail Kapralov

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial 2-approximation for this problem that uses only O(log n) space, namely, count the number of edges and output hal ...

ASSOC COMPUTING MACHINERY2019