On the Complexity of Polytopes in $LI(2)$

Komei Fukuda; May Szedlak

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arXiv · 1706.10114

On the Complexity of Polytopes in $LI(2)$

Komei Fukuda·May Szedlak

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Abstract

In this paper we consider polytopes given by systems of $n$ inequalities in $d$ variables, where every inequality has at most two variables with nonzero coefficient. We denote this family by $LI(2)$. We show that despite of the easy algebraic structure, polytopes in $LI(2)$ can have high complexity. We construct a polytope in $LI(2)$, whose number of vertices is almost the number of vertices of the dual cyclic polytope, the difference is a multiplicative factor of depending on $d$ and in particular independent of $n$. Moreover we show that the dual cyclic polytope can not be realized in $LI(2)$.

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BibTeX RIS

Komei Fukuda, May Szedlak. 2017-06-30. On the Complexity of Polytopes in $LI(2)$. https://arxiv.org/abs/1706.10114

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