Fast approximations for combinatorial optimization via multiplicative weight updates

"We develop fast approximations for several LP relaxations that arise in discrete and combinatorial optimization. New results include improved running times for explicit mixed packing and covering problems, nearly linear time approximations for tree packings, nearly linear time approximations for the Held Karp bound (leading to a significantly faster (3/2 + ε)-approximation for metric TSP), faster approximations for covering LPs with knapsack covering constraints (the bottleneck for covering integer programs), and nearly linear time (2+ε)-approximations for $k$-cut via the LP. Along the way we develop new techniques for the MWU framework and put forth two frameworks, ""lazy MWU"" for deterministic algorithms and ""randomized MWU"" for randomized algorithms, that algorithm designers can use to obtain nearly linear running times for their own problems of interest. This thesis has been organized as a user friendly guide, where we include basic background and analysis of the MWU framework, establish clean interfaces for the two frameworks, and use the applications as examples of the frameworks."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Quanrud, Kent

Contributors dc:contributor

• Chekuri, Chandra
• Har-Peled, Sariel
• Erickson, Jeff
• Young, Neal E
• Blum, Avrim

• Approximation algorithms
• Linear programming
• Combinatorial optimization
• fast approximations
• traveling salesman problem

Statement dc:rights

• Copyright 2019 Kent Quanrud

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106153

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106153