Forbidden vertices
Gustavo Angulo, Shabbir Ahmed, Santanu S. Dey, Volker Kaibel

TL;DR
This paper introduces the forbidden-vertices problem, analyzing its complexity and tractability depending on polytope encoding, with applications to binary and integral polytopes.
Contribution
It defines the forbidden-vertices problem, explores its complexity, and provides new tractability results and formulations for specific polytope classes.
Findings
Complexity varies with polytope and subset encoding.
Extended formulations improve tractability for binary polytopes.
Applications to integral polytopes are discussed.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicsgraph theory and CDMA systems · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
