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Forbidden vertices

In this work, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This problem is closely related to finding the k-best basic solutions to a linear problem. We show that the complexity of the problem changes significantly depending on the encoding of both P and X. We provide additional tractability results and extended formulations when P has binary vertices only. Some applications and extensions to integral polytopes are discussed.

preprint2014arXivOpen access
Gustavo AnguloShabbir AhmedSantanu S. DeyVolker Kaibel
math.COmath.OC
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Open access4 authors2 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Gustavo AnguloShabbir AhmedSantanu S. DeyVolker Kaibel

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