redund - Man Page

Name

redund|minrep  -   Remove redundant inequalities from an H-representation or redundant vertices (non-extreme points) from a V-representation. minrep also identifies hidden linearities.

Synopsis

redund [input-file] [output-file]      

minrep [input-file] [output-file]    

mpirun -np [procs] mplrs -minrep [input-file] [output-file] [option...]

Description

redund and minrep are aliases to lrs which is part of  the C library lrslib(5).  This functionality can also be performed by lrs directly by using the options described below. All computations are done in exact arithmetic. For input file descriptions see lrs(1). A parallel version of minrep is given by mplrs -minrep.  The -redund option performs the same function and is retained for legacy. (see mplrs(1))

redund
H-representation: redundant inequalities in an input H-representation are removed and the remaining inequalities output.  Hidden linearities are not detected unless the testlin option is included, in which case the output is a minimum representation and the dimension is reported.
V-representation: outputs all extreme points and extreme rays, often called the convex hull problem.  The testlin option cause linearities to be detected and explicitly output.
Outputs can be piped directly into lrs. redund is a link to lrs which can also perform these functions via  the testlin, redund and redund_list options.  mplrs -redund always sets the testlin option, so always produces minimum representations.

minrep
Equivalent to redund with the testlin option.

With no options minrep|redund will process the entire input file.

redund start end      
Check input lines with line numbers from start to end and remove any redundant lines.
redund 0 0  will check all input lines.

redund_list k   i_1 i_2 ... i_k  
Check the k input line numbers with indices i_1 i_2 ... i_k   and remove any redundant lines.

testlin      (before the begin line only)   (new 7.3)
redund An LP test will be made for hidden linearities at the beginning of the run and is reported. If there are no hidden linearities one LP per constraint tests for redundancy. If hidden linearities exist two LPs per constraint search for hidden linearities and remove redundancies. In both cases the run ends with a minimum set of linearities and inequalities (ie. no hidden inequalities or duplicates) and the dimension is reported.
lrs If neither redund or redund_list options are present the initial LP test is made, reported and the run halted. Otherwise as above for redund.
mplrs This option is ignored. In redund/minrep mode a minimum representation is always found.

verbose
As each input line is checked a message is printed telling its status
*nr :non-redundant
*re :redundant
*sr :strongly redundant
For an H-representation strongly redundant means the feasible region lies in its open half-space. For a V-representation it means that the point lies in the (relative) interior of the convex hull.
In addition minrep may report
*li :linearity

Examples

(1) Remove hidden linearities and minimum representation of an H-representation.
% cat cube.ine
H-representation
begin
7 4 rational
 0  1  0  0
 0  0  1  0
 0  0  0  1
 1 -1  0  0
 1  0 -1  0
 1  0  0 -1
-1  0  0  1
end
verbose

% minrep cube.ine
minrep:lrslib_v.7.3_2024.1.10(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from  cube.ine
*hidden linearities exist
*finding minimum representation
*nr 0  1  0  0
*nr 0  0  1  0
*sr 0  0  0  1
*nr 1 -1  0  0
*nr 1  0 -1  0
*li 1  0  0 -1
*li-1  0  0  1
*linearity in row=6 removed or in cobasis, independent
*linearity in row=7 dependent, made redundant
H-representation
linearity 1 1
begin
5 4 rational
 1  0  0 -1
 0  1  0  0
 0  0  1  0
 1 -1  0  0
 1  0 -1  0
end

*input had 7 rows and 4 columns
* 2 redundant row(s) found
 3 7
* 1 hidden linearity found

(2) Compute the extreme points of a set of 10 points in R^3

% cat c.ext
V-representation
begin
10 4 rational
1  1  1  1
1  0  1  1
1 1/2 0 1/3
1  1  1  0
1  0  1  0
1  1  0  0
1  0  0  0
1  0 1/3 1/4
1  1  0  1
1  0  0  1
end

% redund c.ext

*redund:lrslib v.7.2 2020.6.8(64bit,lrslong.h,hybrid arithmetic)
*Input taken from  c.ext
V-representation
begin
8 4 rational
1  1  1  1
1  0  1  1
1  1  1  0
1  0  1  0
1  1  0  0
1  0  0  0
1  1  0  1
1  0  0  1
end
*Input had 10 rows and 4 columns
* 2 redundant row(s) found:
3 8

Notes

1. FAQ page
   https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
2. redund: extreme point enumeration and eliminating redundant inequalities
   http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html#redund
3. User's guide for lrslib
   http://cgm.cs.mcgill.ca/%7Eavis/C/lrslib/USERGUIDE.html

Author

David Avis <avis at cs dot mcgill dot ca >

See also

lrs(1), mplrs(1), lrslib(5),