NAME

       lrslib: Convert between representations of convex polyhedra, remove redundant inequalities, convex hull
       computation, solve linear programs in exact precision, compute Nash-equibria in 2-person games.

SYNOPSIS

       lrs [input-file] [output-file]

       redund [input-file] [output-file]

       mpirun -np num-proc mplrs input-file [output-file] [options]

       lrsnash [options] [input-file]

       hvref/xvref [input-file]

DESCRIPTION

       A polyhedron can be described by a list of inequalities (H-representation) or as by a list of its
       vertices and extreme rays (V-representation).  lrslib is a C library containing programs to manipulate
       these representations.  All computations are done in exact arithmetic.

       lrs converts an H-representation of a polyhedron to its V-representation and vice versa, known
       respectively as the vertex enumeration and facet enumeration problems (see Example (1) below).  lrs can
       also be used to solve a linear program, remove linearities from a system, and extract a subset of
       columns.

       redund removes redundant inequalities in an input H-representation and outputs the remaining
       inequalities.  For a V-representation input it outputs all extreme points and extreme rays. Both outputs
       can be piped directly into lrs.  redund is a link to lrs which performs these functions via the redund
       and redund_list options.

       mplrs is Skip Jordan's parallel wrapper for lrs/redund.

       lrsnash is Terje Lensberg's application of lrs for finding Nash-equilibria in 2-person games.

       hvref/xvref produce a cross reference list between H- and V-representations.

ARITHMETIC

       From version 7.1 lrs/redund/mplrs use hybrid arithmetic with overflow checking, starting in 64bit
       integers, moving to 128bit (if available) and then GMP.  Overflow checking is conservative to improve
       performance: eg. with 64 bit arithmetic, a*b triggers overflow if either a or b is at least 2^31, and a+b
       triggers an overflow if either a or b is at least 2^62.  Typically problems that can be solved in 64bits
       run 3-4 times faster than with GMP and inputs solvable in 128bits run twice as fast as GMP.

       Various arithmetic versions are available and can be built from the makefile:

NOTES

       User's guide for lrslib
           http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html

AUTHOR

       David Avis <avis at cs dot mcgill dot ca >

SEE ALSO

       lrs(1), mplrs(1), lrsnash(1),