English

Forbidden vertices

Optimization and Control 2014-03-04 v2 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1309.2545,
  title  = {Forbidden vertices},
  author = {Gustavo Angulo and Shabbir Ahmed and Santanu S. Dey and Volker Kaibel},
  journal= {arXiv preprint arXiv:1309.2545},
  year   = {2014}
}

Comments

15 pages

R2 v1 2026-06-22T01:24:15.718Z