Linear algebraic techniques in algorithms and complexity

We develop linear algebraic techniques in algorithms and complexity, and apply them to a variety of different problems. We focus in particular on matrix multiplication algorithms, which have surprisingly fast running times and can hence be used to design fast algorithms in many settings, and matrix rank methods, which can be used to design algorithms or prove lower bounds by analyzing the ranks of matrices corresponding to computational tasks. First, we study the design of matrix multiplication algorithms. We define a new general method, called the Universal Method, which subsumes all the known approaches to designing these algorithms. We then design a suite of techniques for proving lower bounds on the running times which can be achieved by algorithms using many tensors and the Universal Method.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Alman, Josh(Joshua H.)

Advisor dc:contributor.advisor

• R. Ryan Williams and Virginia Vassilevska Williams.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/124111

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/124111