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Proceedings
SIAM Conference on Applied and Computational Discrete Algorithms (ACDA23)

Integer Programming for the Maximum Cut Problem: A Refined Model and Implications for Branching

Abstract

We present a refined integer programming model for the Maximum Cut problem along with new and extended structural results. Through the relationship between odd-cycle inequalities and parity constraints we uncover a fast separation routine, and a further analysis of the impact of partitioning decisions leads to a new branching rule. In our computational comparison of branching strategies, we demonstrate a significant impact of our model and techniques on state-of-the-art branch-and-cut algorithms and show that our branching rule improves over previous problem-specific ones.

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cover image Proceedings
SIAM Conference on Applied and Computational Discrete Algorithms (ACDA23)
Pages: 63 - 74
Editors: Jonathan Berry, Sandia National Laboratories, USA , David Shmoys, Cornell University, USA , Lenore Cowen, Tufts University, USA , and Uwe Naumann, RWTH Aachen University, Germany
ISBN (Online): 978-1-61197-771-4

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Published online: 15 May 2023

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