PORTA

PORTA is a collection of routines for analyzing polytopes and polyhedra. The polyhedra are either given as the convex hull of a set of points plus (possibly) the convex cone of a set of vectors, or as a system of linear equations and inequalities. The name PORTA is an abbreviation for POlyhedron Representation Transformation Algorithm and points to the basic function ’traf’. This function performs a transformation from one of the two representations to the other representation. For this, ’traf’ uses a Fourier - Motzkin elimination algorithm which projects a linear system on subspaces xi = 0. This projection of a given system of linear inequalities can be done separately by using the function ’fmel’. ...


References in zbMATH (referenced in 121 articles , 1 standard article )

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  1. David Avis, Charles Jordan: lrsarith: a small fixed/hybrid arithmetic C library (2021) arXiv
  2. Letchford, Adam N.; Vu, Anh N.: Facets from gadgets (2021)
  3. Abramsky, Samson: Classical logic, classical probability, and quantum mechanics (2020)
  4. Heck, Daniel W.; Davis-Stober, Clintin P.: Multinomial models with linear inequality constraints: overview and improvements of computational methods for Bayesian inference (2019)
  5. Hildenbrandt, Achim: A branch-and-cut algorithm for the target visitation problem (2019)
  6. Kim, Jinhak; Tawarmalani, Mohit; Richard, Jean-Philippe P.: On cutting planes for cardinality-constrained linear programs (2019)
  7. Walteros, Jose L.; Veremyev, Alexander; Pardalos, Panos M.; Pasiliao, Eduardo L.: Detecting critical node structures on graphs: a mathematical programming approach (2019)
  8. Arslan, Okan; Jabali, Ola; Laporte, Gilbert: Exact solution of the evasive flow capturing problem (2018)
  9. Ben-Ameur, Walid; Glorieux, Antoine; Neto, José: Complete formulations of polytopes related to extensions of assignment matrices (2018)
  10. Davis-Stober, Clintin P.; Doignon, Jean-Paul; Fiorini, Samuel; Glineur, François; Regenwetter, Michel: Extended formulations for order polytopes through network flows (2018)
  11. Deza, Michel; Dutour Sikirić, Mathieu: The hypermetric cone and polytope on eight vertices and some generalizations (2018)
  12. Doostmohammadi, Mahdi; Akartunalı, Kerem: Valid inequalities for two-period relaxations of big-bucket lot-sizing problems: zero setup case (2018)
  13. Fairbrother, Jamie; Letchford, Adam N.; Briggs, Keith: A two-level graph partitioning problem arising in mobile wireless communications (2018)
  14. Gläßle, T.; Gross, D.; Chaves, R.: Computational tools for solving a marginal problem with applications in Bell non-locality and causal modeling (2018)
  15. Moazzez, Babak; Soltani, Hossein: Integer programming approach to static monopolies in graphs (2018)
  16. Aguilera, Néstor E.; Katz, Ricardo D.; Tolomei, Paola B.: Vertex adjacencies in the set covering polyhedron (2017)
  17. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with \textttpolymake (2017)
  18. Moeini, Asghar: Identification of unidentified equality constraints for integer programming problems (2017)
  19. Pecin, Diego; Pessoa, Artur; Poggi, Marcus; Uchoa, Eduardo; Santos, Haroldo: Limited memory rank-1 cuts for vehicle routing problems (2017)
  20. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)

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