2L_enum swMATH ID: 31753 Software Authors: Bohn, Adam; Faenza, Yuri; Fiorini, Samuel; Fisikopoulos, Vissarion; Macchia, Marco; Pashkovich, Kanstantsin Description: Enumeration of 2-level polytopes. A (convex) polytope P is said to be 2-level 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 2-level polytopes of a given dimension d, and provide complete experimental results for πβ©½7 . Our approach is inductive: for each fixed (πβ1) -dimensional 2-level polytope π0 , we enumerate all d-dimensional 2-level 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 2-level polytopes in dimension d. Homepage: https://rd.springer.com/article/10.1007%2Fs12532-018-0145-6 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; OEIS; plantri; SlackIdeals; Maple; nauty; uBLAS; Boost; Traces; Boost C++ Libraries; Algorithm 457; CPAN; CRAN Cited in: 15 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Enumeration of 2-level polytopes. Zbl 1414.05023Bohn, Adam; Faenza, Yuri; Fiorini, Samuel; Fisikopoulos, Vissarion; Macchia, Marco; Pashkovich, Kanstantsin 2019 all top 5 Cited by 23 Authors 5 Faenza, Yuri 5 Fiorini, Samuel 5 Macchia, Marco 4 Aprile, Manuel 4 Gouveia, Joao 3 Fisikopoulos, Vissarion 3 Pashkovich, Kanstantsin 2 Bogart, Tristram 2 Bohn, Adam 2 Cevallos, Alfonso 2 Kupavskii, Andrey 2 Thomas, Rekha R. 2 Torres, Juan Camilo 1 Conforti, Michele 1 Huynh, Tony 1 Macchia, Antonio 1 Noskov, Fedor 1 Pashkovich, Kanstanstin 1 Pichugina, O. S. 1 Robinson, Richard Z. 1 Weltge, Stefan 1 Wiebe, Amy 1 Yakovlev, Sergey V. all top 5 Cited in 10 Serials 2 Journal of Combinatorial Theory. Series B 2 Discrete & Computational Geometry 1 Discrete Applied Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal of Pure and Applied Algebra 1 Operations Research Letters 1 SIAM Journal on Discrete Mathematics 1 Cybernetics and Systems Analysis 1 Journal of Algebra and its Applications 1 Mathematical Programming Computation all top 5 Cited in 7 Fields 11 Convex and discrete geometry (52-XX) 7 Combinatorics (05-XX) 7 Operations research, mathematical programming (90-XX) 3 Commutative algebra (13-XX) 3 Computer science (68-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) Citations by Year