PORTA swMATH ID: 4869 Software Authors: Christof, T.; Reinelt, G.; Andreas Loebel Description: 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’. ... Homepage: https://wwwproxy.iwr.uni-heidelberg.de/groups/comopt/software/PORTA/ Keywords: special polytopes; double-description method; computational geometry; hard combinatorial optimization; branch-and-cut method; facet structure; traveling salesman; linear ordering polytopes Related Software: LOLIB; cdd; CPLEX; TSPLIB; polymake; ABACUS; Normaliz; Concorde; lrs; nauty; MIPLIB; Macaulay2; Mathematica; GitHub; SCIP; Gurobi; VRP; QTest; PPL; Magma Cited in: 131 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Combinatorial optimization and small polytopes. Zbl 0858.90107Christof, T.; Reinelt, G. 1996 all top 5 Cited by 219 Authors 11 Reinelt, Gerhard 9 Doignon, Jean-Paul 6 Fiorini, Samuel 6 Letchford, Adam N. 5 Christof, Thomas 5 Schürmann, Achill 4 Davis-Stober, Clintin P. 4 Dutour-Sikiric, Mathieu 4 Fischetti, Matteo 4 Lodi, Andrea 4 Richard, Jean-Philippe Pascal 4 Villarreal, Rafael Heraclio 4 Wenger, Klaus Michael 3 Charon, Irène 3 Christophe, Julie 3 Doostmohammadi, Mahdi 3 Galluccio, Anna 3 Gentile, Claudio 3 Hudry, Olivier 3 Jünger, Michael 3 Marenco, Javier L. 3 Moeckel, Richard 3 Nemhauser, George L. 3 Regenwetter, Michel 3 Tawarmalani, Mohit 3 Theis, Dirk Oliver 3 Yaman, Hande 2 Agra, Agostinho 2 Aguilera, Néstor E. 2 Chaves, Rafael 2 Deza, Michel Marie 2 Fishburn, Peter Clingerman 2 Gawrilow, Ewgenij 2 Hampton, Marshall 2 Joswig, Michael 2 Koch, Ivo 2 Köppe, Matthias 2 Laporte, Gilbert 2 Martí, Rafael 2 Neto, José 2 Pardalos, Panos M. 2 Rinaldi, Giovanni 2 Vallentin, Frank 2 Ventura, Paolo 2 Wolsey, Laurence Alexander 1 Abramsky, Samson 1 Acin, Antonio 1 Adams, Elspeth 1 Adams, Warren Philips 1 Agarwal, Yogesh Kumar 1 Akartunalı, Kerem 1 Aneja, Yash P. 1 Anjos, Miguel F. 1 Antreich, Kurt J. 1 Applegate, David L. 1 Arslan, Okan 1 Ascheuer, Norbert 1 Assarf, Benjamin 1 Bachmaier, Christian 1 Ballerstein, Martin 1 Balof, Barry A. 1 Bastrakov, Sergeĭ Ivanovich 1 Bektas, Tolga 1 Ben-Ameur, Walid 1 Benoit, Geneviève 1 Bixby, Robert E. 1 Bondarenko, V. A. 1 Bougnol, Marie-Laure 1 Boyd, Sylvia C. 1 Brandenburg, Franz-Josef 1 Bremner, David 1 Briggs, Keith M. 1 Brown, Nicholas F. 1 Buchheim, Christoph 1 Burchett, D. L. 1 Cacchiani, Valentina 1 Cavagnaro, Daniel R. 1 Chung, Kwanghun 1 Churkin, A. V. 1 Chvátal, Václav 1 Conforti, Michele 1 Cook, William John 1 Cordeau, Jean-François 1 Csirmaz, László 1 Dash, Sanjeeb 1 de Klerk, Etienne 1 de Souza, Cid Carvalho 1 Del Carmen Varaldo, María 1 Dewez, Sophie 1 Deza, Elena Ivanovna 1 Di Summa, Marco 1 Dietz, Audrey 1 Duarte, Abraham 1 Dulá, José H. 1 Dumitrescu, Irina 1 Eglese, Richard W. 1 Elf, Matthias 1 Elloumi, Sourour 1 Escalante, Mariana S. 1 Fairbrother, Jamie ...and 119 more Authors all top 5 Cited in 53 Serials 15 Mathematical Programming. Series A. Series B 9 Discrete Applied Mathematics 8 Journal of Mathematical Psychology 7 Discrete Optimization 5 European Journal of Operational Research 4 Mathematics of Operations Research 3 Discrete Mathematics 3 Networks 3 European Journal of Combinatorics 3 Operations Research Letters 3 Computational Optimization and Applications 3 EURO Journal on Computational Optimization 2 Transactions of the American Mathematical Society 2 Order 2 Annals of Operations Research 2 Journal of Combinatorial Optimization 2 New Journal of Physics 2 Optimization Letters 1 Computer Physics Communications 1 Mathematics of Computation 1 INFOR 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of Combinatorial Theory. Series B 1 Kybernetika 1 Operations Research 1 Software. Practice & Experience 1 Optimization 1 Journal of Symbolic Computation 1 Algorithmica 1 Discrete & Computational Geometry 1 Computers & Operations Research 1 International Journal of Computational Geometry & Applications 1 Automation and Remote Control 1 Linear Algebra and its Applications 1 SIAM Journal on Optimization 1 Journal of Algebraic Geometry 1 Finite Fields and their Applications 1 Top 1 Electronic Research Announcements of the American Mathematical Society 1 International Transactions in Operational Research 1 INFORMS Journal on Computing 1 Optimization Methods & Software 1 Mathematical Methods of Operations Research 1 Journal of Graph Algorithms and Applications 1 RAIRO. Operations Research 1 4OR 1 Applied Mathematical Sciences 1 University Lecture Series 1 Journal of Physics A: Mathematical and Theoretical 1 Mathematical Programming Computation 1 Research in the Mathematical Sciences 1 Discrete Mathematics and its Applications all top 5 Cited in 21 Fields 89 Operations research, mathematical programming (90-XX) 31 Convex and discrete geometry (52-XX) 27 Combinatorics (05-XX) 15 Computer science (68-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Number theory (11-XX) 5 Order, lattices, ordered algebraic structures (06-XX) 4 Commutative algebra (13-XX) 4 Quantum theory (81-XX) 4 Information and communication theory, circuits (94-XX) 3 Algebraic geometry (14-XX) 3 Geometry (51-XX) 3 Statistics (62-XX) 3 Mechanics of particles and systems (70-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 1 Group theory and generalizations (20-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX) Citations by Year