Discrete and
Combinatorial Optimization

## PORTA Vers. 1.4.1 (win32 binaries and Linux SuSE 8.1 rpm package available)

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'.

Sometimes it is of interest to know all integral points contained in a polyhedron which is given by a system of linear equations and inequalities. For this one has the function 'vint' which enumerates all the valid integral points within given bounds. As a special function in this context 'fctp' checks the facet inducing property of a set of linear inequalities for a polyhedron given as a convex hull plus a convex cone. The function 'fctp' uses a function 'dim', which computes the dimension of a polyhedron given as a convex hull plus a convex cone. Finally 'portsort' is helpful to make datafiles readable. portsort sorts and formats given systems.

All functions read and write the data from and to files. Such files can be manipulated by the user with a default texteditor. PORTA guarantees correct numerical results, because only integer operations are performed. If an arithmetic overflow occurs with the systems integer arithmetic then the computations can be restarted with a double precision integer arithmetic.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
Thomas Christof
T.Christof@deutschepost.de
Sebastian Schenker
Konrad-Zuse-Zentrum fuer
Informationstechnik (ZIB)
Takustr. 7
D-14195 Berlin-Dahlem
schenker@zib.de

Mod. 17.09.15, CP Erstellt am Wed Aug 6 16:39:13 2008
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