mplrs(1)

🌸 mplrs — the polyhedra glow-up page 💅

okay bestie, welcome to mplrs from the mplrs 7.3 manual ✨

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✨ NAME ✨

mplrs — convert between representations of convex polyhedra, remove redundant inequalities, do Fourier-Motzkin elimination (parallel version, no cap 🧚)

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🌈 SYNOPSIS 🌈

mpirun  -np num_proc mplrs infile [outfile] [option...]

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💖 DESCRIPTION 💖

so. a polyhedron can be described either by a list of inequalities (that's the H-representation) or by a list of its vertices and extreme rays (that's the V-representation). mplrs is literally the parallel version of lrs, and it converts an H-representation of a polyhedron to its V-representation, and vice versa. those two problems are known as the vertex enumeration and convex hull problems respectively 🫶

if you've got the lrs options redund or redund_list in the input file, it'll do parallel execution of minrep (computing a minimum representation), see redund(1) 💜

and if you've got the lrs options project or eliminate in the input file, it'll do parallel execution of fel (Fourier-Motkin elimination) 🔥

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🎀 USAGE 🎀

the number of processors num_proc you hand to mpirun should be 4 or higher. lowkey important. also some lrs input file options are just not supported by mplrs, so don't come for me 🙈

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✨ OPTIONS ✨

mplrs supports the following options, and the default values are chillin' in brackets:

• -checkp <checkpoint file> — if mplrs gets terminated by -stop or -time, you can restart it using this <checkpoint file> and -restart 💾
• -countonly — don't output vertices/rays/facets, just count them. minimal effort, iconic behaviour 👑
• -freq <file> — store frequency data in <file> for use by gnuplot, see below 📈
• -hist <file> — store parallelization data in <file> for use by gnuplot, see below 📊
• -id <initial depth> — [2] the depth of the original tree search to populate the job list L 🌳
• -lmax <int> — [lmin] if job list |L|>np*lmax then maxc is replaced by maxc*scale
• -lmin <int> — [3] if job list |L|<np*lmin then the maxd parameter is set for all producers
• -maxbuf <n> — [500] controls maximum size of worker output buffers
• -maxc <maxcobases> — [50 (*scale)] a producer stops and returns all subtrees that are not leaves to L after generating maxc nodes
• -maxd <depth> — [0] a producer returns all subtrees that are not leaves at depth maxd. Zero if not used
• -minheight — jobs are scheduled in increasing order by height in the search tree (default is LIFO)
• -queue — jobs are scheduled in FIFO order (default is LIFO)
• -restart <checkpoint file> — restart mplrs using previously created <checkpoint file>. If used with -checkp file names should be different! ⚠️
• -scale <int> — [100] used by lmax
• -stop <stopfile> — terminate mplrs if a file with name <stopfile> is created in the current directory 🛑
• -stopafter <n> — exit after approximately <n> cobases have been computed (no guarantee about how many vertices/rays/facets computed)
• -temp <prefix> — [/tmp/] store a temporary file for each process. Should be specified if /tmp not writeable. Using " -temp ./ " will write temporary files to the current directory
• -time <seconds> — terminate mplrs after <seconds> of elapsed time ⏰

🌸 redund/fel options 🌸

• -j <int> — [1] if non-zero splits the run into <int> jobs per worker, over-riding rows and lastrows
• -lastp <int> — [10] the percentage of jobs to use lastrows
• -lastrows <int> — [10] the number of rows for the last lastp jobs
• -minrep — removes redundant inequalities, finds hidden linearities and outputs a minimum representation of the input file. This ignores any project or eliminate option present in the input file
• -rows <int> — [60] the number of rows per job

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💜 -hist file format 💜

example line, bestie:

54.118141 94 279 94 0 0 373

here's the tea on what each one means:

• time since execution began in seconds (54.118141 here)
• number of busy workers (94 here)
• current size of job list (279 here)
• number of workers that may return unfinished jobs (94 here)
• unused (0 here)
• unused (0 here)
• total number of jobs that have been in the job list (373 here)

the second and fourth entries are similar and can differ due to latencies 🦋

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🍓 -freq file format 🍓

one integer per line corresponding to the size of a subtree explored by a worker.

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⭐ EXAMPLE ⭐

input file mp5.ine is run with 8 processors. this produced 378 subtrees that were enumerated in parallel using 6 producer cores, 1 core controlling the run and 1 core collecting the output. slay.

mai20% mpirun -np 8 mplrs mp5.ine mp5.mplrs
*mplrs:lrslib v.6.0 2015.7.13(lrsgmp.h)8 processes
*Copyright (C) 1995,2015, David Avis   avis@cs.mcgill.ca
*Input taken from mp5.ine
*Output written to: mp5.mplrs
*Starting depth of 2 maxcobases=50 maxdepth=0 lmin=3 lmax=3 scale=100
*Phase 1 time: 0 seconds.
*Total number of jobs: 378, L became empty 4 times
*Totals: vertices=32 rays=0 bases=9041 integer-vertices=16
*Elapsed time: 1 seconds.
2.285u 0.137s 0:01.86 129.5%    0+0k 0+9976io 36pf+0w

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🎀 AUTHOR 🎀

Charles Jordan <skip at res dot otaru-uc dot ac dot jp > — we stan 💖

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🫶 SEE ALSO 🫶

lrs(1), lrslib(5)

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and that's the whole page, periodt ✨ this one is from the mplrs manual, version 2024.2.5, dated February 2024 — okay love u bye, go enumerate some vertices 💅🌸🦋