Date Thesis Awarded

5-2010

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

David Phillips

Committee Member

Michael Lewis

Committee Member

Rex K. Kincaid

Committee Member

Virginia Torczon

Abstract

This thesis investigates various computational approaches to the Maximum Cut problem. It is generally believed that Maximum Cut cannot be solved exactly in polynomial time, so we approach the problem using various heuristics and approximation algorithms. We introduce a rank-penalization heuristic that generates feasible solutions to Maximum Cut. Numerical results show that these solutions are comparable to those given by the Goemans-Williamson randomized algorithm. We also implement a branch and bound algorithm using a branching scheme based on optimal dual variables for the Maximum Cut semidefinite programming relaxation. In our test cases, the dual branching scheme performed consistently better than randomized or largest-degree branching schemes.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

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