2L_enum
swMATH ID:  31753 
Software Authors:  Bohn, Adam; Faenza, Yuri; Fiorini, Samuel; Fisikopoulos, Vissarion; Macchia, Marco; Pashkovich, Kanstantsin 
Description:  Enumeration of 2level polytopes. A (convex) polytope P is said to be 2level if for each hyperplane H that supports a facet of P, the vertices of P can be covered with H and exactly one other translate of H. The study of these polytopes is motivated by questions in combinatorial optimization and communication complexity, among others. In this paper, we present the first algorithm for enumerating all combinatorial types of 2level polytopes of a given dimension d, and provide complete experimental results for πβ©½7 . Our approach is inductive: for each fixed (πβ1) dimensional 2level polytope π0 , we enumerate all ddimensional 2level polytopes P that have π0 as a facet. This relies on the enumeration of the closed sets of a closure operator over a finite ground set. By varying the prescribed facet π0 , we obtain all 2level polytopes in dimension d. 
Homepage:  https://rd.springer.com/article/10.1007%2Fs1253201801456 
Source Code:  https://zenodo.org/record/1405386#.XjvPDMZKjmI 
Keywords:  polyhedral computation; polyhedral combinatorics; optimization; formal concept analysis; algorithm engineering 
Related Software:  01poly; Macaulay2; SageMath; birkhoff faces; polymake; SlackIdeals; Maple; uBLAS; Boost; Traces; Boost C++ Libraries; nauty; CPAN; CRAN 
Cited in:  12 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Enumeration of 2level polytopes. Zbl 1414.05023 Bohn, Adam; Faenza, Yuri; Fiorini, Samuel; Fisikopoulos, Vissarion; Macchia, Marco; Pashkovich, Kanstantsin 
2019

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Cited by 20 Authors
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Cited in 8 Serials
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