Living with lrs. This paper describes the development of lrs, an implementation of the reverse search method to the verter enumeration/conver hull problem for conver polyhedra. We describe an important and difficult class of polyhedra, called configuration polytopes, that have application to determining the ground states of alloy phase diagrams. Experience gained while trying to solve these problems lead to a number of improvements to the original implementation.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Assarf, Benjamin; Gawrilow, Ewgenij; Herr, Katrin; Joswig, Michael; Lorenz, Benjamin; Paffenholz, Andreas; Rehn, Thomas: Computing convex hulls and counting integer points with polymake (2017)
  2. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  3. Avigad, Jeremy; Lewis, Robert Y.; Roux, Cody: A heuristic prover for real inequalities (2016)
  4. Andreas Baechle, Leo Margolis: HeLP -- A GAP-package for torsion units in integral group rings (2015) arXiv
  5. Savani, Rahul; von Stengel, Bernhard: Game Theory Explorer: software for the applied game theorist (2015)
  6. Avis, David; Roumanis, Gary: A portable parallel implementation of the $lrs$ vertex enumeration code (2013)
  7. Joswig, Michael; Theobald, Thorsten: Polyhedral and algebraic methods in computational geometry (2013)
  8. Avis, David; Rosenberg, Gabriel D.; Savani, Rahul; von Stengel, Bernhard: Enumeration of Nash equilibria for two-player games (2010)
  9. Takemura, Akimichi; Yoshida, Ruriko: A generalization of the integer linear infeasibility problem (2008)
  10. Kreuzer, Maximilian; Skarke, Harald: PALP: A package for analysing lattice polytopes with applications to toric geometry (2004)
  11. Emiris, Ioannis Z.: Enumerating a subset of the integer points inside a Minkowski sum (2002)
  12. Gawrilow, Ewgenij; Joswig, Michael: polymake: an approach to modular software design in computational geometry (2001)
  13. Reid, Les; Roberts, Leslie G.: Monomial subrings in arbitrary dimension (2001)
  14. Avis, David: Living with $lrs$ (2000)
  15. Avis, David: Computational experience with the reverse search vertex enumeration algorithm (1998)