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What and Who

A Faster Algorithm for Linear Programming and the Maximum Flow Problem

Yin Tat Lee
MIT
Talk

Yin Tat Lee is a PhD student (under Professor Jonathan Kelner) at MIT, studying theoretical computer science. His areas of research span convex optimization, linear programming, spectral graph theory and algorithmic graph theory. He is particularly interested in combining convex optimization and combinatorial techniques to design fast algorithms for fundamental cut/flow problems. He is one of the recipients of the Best Paper Award at SODA 2014 for an almost-linear-time algorithm for approximate max flow in undirected graphs. Recently, Aaron Sidford and he resolved a long-standing open question for linear programming, which gives a faster interior point method and a faster exact min cost flow algorithm. This result receives the Best Paper Award, as well as the Best Student Paper Award of FOCS 2014.
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AG Audience
English

Date, Time and Location

Tuesday, 20 January 2015
13:00
60 Minutes
E1 4
024
Saarbrücken

Abstract

In this talk, I will present a new algorithm for solving linear programs. Given a linear program with n variables, m > n constraints, and bit complexity L, our algorithm runs in Õ(sqrt(n) L) iterations each consisting of solving Õ(1) linear systems and additional nearly linear time computation. Our method improves upon the convergence rate of previous state-of-the-art linear programming methods which required solving either Õ(sqrt(m)L) linear systems [R88] or consisted of Õ((mn)^(1/4)) steps of more expensive linear algebra [VA93].

Interestingly, our algorithm not only nearly matches the convergence rate of the universal barrier of Nesterov and Nemirovskii [NN94], but in the special case of the linear programming formulation of various flow problems our methods converge at a rate faster than that predicted by any self-concordant barrier. In particular, we achieve a running time of Õ(|E| sqrt(|V|) log^2 U) for solving the maximum flow problem on a directed graph with |E| edges, |V| vertices, and capacity ratio U, thereby improving upon the previous fastest running time for solving this problem when |E| > Ω(|V|^(1+epsilon)) for any constant epsilon.

This talk will assume little exposure to linear programming algorithms, convex optimization, or graph theory.

This talk reflects joint work with Aaron Sidford.

See http://arxiv.org/abs/1312.6677 and http://arxiv.org/abs/1312.6713.

Contact

He Sun
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Video Broadcast

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He Sun, 01/20/2015 10:04
He Sun, 01/19/2015 09:20
He Sun, 12/04/2014 08:40
He Sun, 12/04/2014 07:25 -- Created document.