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The Maximum Cut Problem: Investigating Computational Approaches
Powell, Austin
Powell, Austin
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.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2010-05-17
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Keywords
Max Cut, Semidefinite Programming, Optimization, Branch and Bound
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Advisor
Phillips, David
Lewis, Michael
Kincaid, Rex K.
Torczon, Virginia
Lewis, Michael
Kincaid, Rex K.
Torczon, Virginia
Department
Mathematics