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Semidefinite programming approaches for stable set and max-cut problems
Sinjorgo,Lennart
Sinjorgo,Lennart
Abstract
This thesis investigates the use of semidefinite programming (SDP) for solving (variants of) the well-known stable set and max-cut problems. Chapter 2 considers a generalization of the stable set problem, and a corresponding SDP relaxation. Similarly, Chapter 3 considers a generalization of the max-cut problem that involves complex roots of unity. Various complex SDP relaxations of this generalized max-cut problem are studied. Chapter 4 provides approximation algorithms for the quantum generalization of the max-cut problem. These approximation algorithms employ a hierarchy of SDP relaxations for noncommutative polynomial optimization problems. Chapter 5 provides an SDP algorithm for computing bounds on the stability numbers of graphs. Chapter 6 provides an SDP algorithm for solving the MAX-SAT problem. Chapters 5 and 6 provide extensive numerical results on these algorithms.
Description
CentER Dissertation Series Volume: 789
Date
2026
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CentER
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Citation
Sinjorgo, L 2026, 'Semidefinite programming approaches for stable set and max-cut problems', Doctor of Philosophy, Tilburg University, Tilburg. https://doi.org/10.26116/tisem.63859127
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info:eu-repo/semantics/openAccess