====== mptopcom ======

**mptopcom** is a software developed at TU Berlin and Hokkaido University for computing triangulations of point configurations in parallel. It is a combination of

  * **[[http://www.rambau.wm.uni-bayreuth.de/TOPCOM/|TOPCOM]]** for triangulations,
  * **[[https://polymake.org/doku.php|polymake]]** for combinatorics, and
  * **[[http://cgm.cs.mcgill.ca/~avis/doc/tutorial.html|mts]]** for parallelising reverse search.

Our **[[https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i3p6|paper]]** describes the algorithm and contains many details as well as examples. Please cite this reference in your papers if you are using mptopcom.

===== Prerequisites =====

Please read this very carefully! mptopcom is highly optimized software dedicated to exceptionally large enumerations on suitable hardware. As a consequence it depends on a number of up-to-date-versions of other software, and the installation requires some diligence.

You need to have **[[https://www.open-mpi.org/|open-mpi]]** or some other mpi implementation and **[[https://polymake.org/doku.php|polymake]]** version at least 4.11 installed. In particular, you need the **[[https://polymake.org/doku.php/reference/callable|polymake callable library]]**, which might not be installed by the package manager of your distribution. Furthermore, you need an installation of **[[https://www.inf.ethz.ch/personal/fukudak/cdd_home/|cdd]]**, the bundled version coming with polymake does not build the cdd library.

**Note** Having multiple versions of openmpi installed is a common source of errors. During the configuration, mptopcom will display the version of openmpi it found. Please make sure that this version, and the versions of ''%%mpirun%%'', ''%%mpicc%%'', and ''%%mpicxx%%'' all agree, and ideally come from the same installation.

===== Known working configurations =====

==== mptopcom 1.4 ====

  * gcc 11.3.0, openmpi 4.1.5, polymake 4.11
  * clang 18.1.1, openmpi 4.1.5, polymake 4.11

==== mptopcom 1.3 ====

  * gcc 12.2.1, openmpi 4.1.5, polymake 4.9
  * gcc 7.5.0, openmpi 3.1.2-15, polymake 4.6
  * gcc 7.5.0, openmpi 4.1.4, polymake 4.6
  * gcc 7.5.0, openmpi 4.1.4, polymake 4.1

==== Legacy: mptopcom-1.0 – 1.2 ====

**mptopcom** has been tested with several versions, at least 5.3.0, of gcc and clang, at least version 3.8.0. For MPI we have tested openmpi at least version 1.4.1 and Intel MPI 20150128.

===== Download =====

Here are download links to tarballs containing the sources of **mptopcom**:

  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.4.tar.bz2|mptopcom-1.4.tar.bz2]] from 2024-03-25.

**Note** that this version of mptopcom contains a new algorithm for traversing the flip graph of regular triangulations, in that it checks flips for regularity rather than triangulations. The new version has been checked extensively, on the 4-cube and the 3-dilated 3-simplex and many others. Nevertheless, please let us know if you encounter any wrong results.

==== Old versions ====

  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.3.tar.bz2|mptopcom-1.3.tar.bz2]] from 2022-09-01.
  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.2.tar.bz2|mptopcom-1.2.tar.bz2]] from 2020-08-28.
  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.1.tar.bz2|mptopcom-1.1.tar.bz2]] from 2019-05-29 for polymake versions before 4.0.
  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.1_polymake4.0.tar.bz2|mptopcom-1.1_polymake4.0.tar.bz2]] from 2020-02-07 for polymake versions after 4.0.
  * [[https://polymake.org/lib/exe/fetch.php/download/mptopcom-1.0r2.tar.bz2|mptopcom-1.0r2.tar.bz2]] from 2018-05-14 with a bugfix for newer polymake.

===== Installation =====

Installation can be done with the following three commands:

<code>
./configure
ninja -C build/Opt -j #CPU's
ninja -C build/Opt install
</code>

There are several options to the ''%%./configure%%'' command that can be viewed with

<code>
./configure --help
</code>

The most important options are

<code>
--with-polymake=/path/to/polymake/installation
--with-mpi=/path/to/mpi/installation
--prefix=/path/to/install/dir
</code>

The configure command will extract most of the information needed from polymake’s ''%%polymake-config%%'' command.

The binaries are in the ''%%build/Opt/bin%%'' folder after building and in the ''%%prefix/bin%%'' folder after installation. Besides the usual **TOPCOM** binaries there are four new binaries:

  * **mptopcom1**: Runs reverse search single threaded.
  * **mptopcom**: Multithreaded reverse search.
  * **canonicalRepresentative**: Compute the canonical representative from the orbit of a triangulation.
  * **randomBFS**: Execute a random breadth first search on the flip-graph of triangulations, only reports the queue sizes.
  * **random_walk**: Execute a random walk, the size can be specified with the ''%%--rw-size%%'' option.

You can test your build by running the testsuite:

<code>
perl testsuite.pl
</code>

==== mpirun ====

We have had many complaints by users that tracked back to multiple versions of openmpi being installed at the same time. Hence the ''%%mpirun%%'' they were using stemmed from a different installation than the one they specified when building mptopcom. To mitigate this issue, mptopcom places a symlink to the correct ''%%mpirun%%'' in the installation.

==== More than 64 points ====

Since ''%%mptopcom%%'' usually is used for enumerating triangulations, which is hard for larger point configurations, certain optimizations have been built which result in mptopcom only being able to handle at most 64 points.

During installation these optimizations may be turned off using

<code>
CXXFLAGS=-DWITH_PM_BITSET ./configure
</code>

The resulting mptopcom installation will be able to deal with more than 64 points, however it will be significantly slower than the mptopcom standard version.

===== Usage =====

Input files are formatted as in TOPCOM, please have a look at the files in the ''%%examples%%'' folder for samples. The points are given homogeneously, i.e. embedded at height one. After the points you can give the generators of a group acting on your point set. Here is the example of the input file for the two-dimensional 0-1-square:

<code>
[
[1,0,0],
[1,0,1],
[1,1,0],
[1,1,1]
]
[
[0,2,1,3],
[3,1,2,0],
[2,3,0,1]
]
</code>

You can then call mptopcom in the following way:

<code>
mpirun -np 5 mptopcom < examples/cube_4.dat
</code>

If you did not run ''%%make install%%'' you can call the binary in the ''%%build/Opt/bin%%'' folder:

<code>
mpirun -np 5 ./build/Opt/bin/mptopcom < examples/cube_4.dat
</code>

This will produce all triangulations of the four dimensional cube.

There are several options you can invoke to modify the behaviour of mptopcom:

==== Options ====

  - ''%%--cyclic-flips%%'' : Use special combinatorial description of the reverse search graph for cyclic polytopes
  - ''%%--full%%'' : Only list full/fine/spanning triangulations
  - ''%%--flip-cache n%%'' : Sets size of flip cache to n (default: 2000)
  - ''%%--make-marked-tree%%'' : Draws a tree with classes having the same node color (''%%mptopcom1%%'' only)
  - ''%%--make-tree%%'' : Will produce polymake code to plot reverse search tree (''%%mptopcom1%%'' only)
  - ''%%--orbit-cache n%%'' : Size of symmetry cache set to n (default: 2000)
  - ''%%--regular%%'' : Only output regular triangulations
  - ''%%--regularity-cache n%%'' : Size of regularity cache set to n (default: 2000)
  - ''%%-v%%'' : verbose (every worker will tell when he found 1000 triangulations)
  - ''%%--central%%'' : Produce only triangulations with maximal gkz[0], depends on ordering of points

==== Budgeting options ====

  - ''%%-maxnodes%%'' only affects the “bumps” at maxnodes and scale*maxnodes.
  - ''%%-scale%%'' sets the scaling factor when we have many jobs available (workers can work longer if we aren’t trying to split jobs)
  - ''%%-maxd%%'' sets the max depth to go to when we don’t have enough jobs available (2 is the default, which is aggressive. 0 disables)
  - ''%%-lmax%%'' sets the point where -scale is used (if |L| > lmax * numproc)
  - ''%%-lmin%%'' sets the point where -maxd is used (if |L| < lmin * numproc)

===== Checkpointing and restarting =====

**mts** supports checkpointing and restarts; if you add options ''%%-checkp file1 -stop file2%%'' then it will periodically check to see if file file2 exists, and if so then it will checkpoint to file1 when convenient (it waits for workers to finish their current jobs first). Then you can restart using option ''%%-restart file1%%'' (and of course can use -checkp & -stop again, but you should give different filenames to the -restart and -checkp options). There is an example in the section below.

===== Sample usage =====

This section contains samples of how to call ''%%mptopcom1%%'' and ''%%mptopcom%%'' using the above options. It is assumed that **mptopcom** was built, but not installed and that the current directory is the root of the source directory.

==== mptopcom1 ====

<code>
./build/Opt/bin/mptopcom1 < examples/cube_3.dat
./build/Opt/bin/mptopcom1 -v < examples/cube_3.dat
./build/Opt/bin/mptopcom1 -v < examples/moae.dat
./build/Opt/bin/mptopcom1 -v --regular < examples/moae.dat
./build/Opt/bin/mptopcom1 -v --regular --full < examples/moae.dat
./build/Opt/bin/mptopcom1 -v --flip-cache 2000 --orbit-cache 2000 < examples/moae.dat
./build/Opt/bin/mptopcom1 -v --make-tree < examples/moae.dat
</code>

==== mptopcom ====

<code>
mpirun -np 8 ./build/Opt/bin/mptopcom < examples/cube_3.dat
mpirun -np 8 ./build/Opt/bin/mptopcom -v < examples/cube_3.dat
mpirun -np 8 ./build/Opt/bin/mptopcom --regular < examples/cube_4.dat
mpirun -np 10 ./build/Opt/bin/mptopcom < examples/lattice_3_3.dat
mpirun -np 10 ./build/Opt/bin/mptopcom --full < examples/lattice_3_3.dat
mpirun -np 10 ./build/Opt/bin/mptopcom --full --flip-cache 2000 --orbit-cache 2000 < examples/lattice_3_3.dat
mpirun -np 10 ./build/Opt/bin/mptopcom < examples/lattice_3_3.dat 1>output.txt 2>error.txt
</code>

The following is an example for checkpointing and restarting:

<code>
mpirun -np 8 ./build/Opt/bin/mptopcom -v -stop stop_file -checkp checkp_file < examples/cube_4.dat
touch stop_file
</code>

Now the state will be written to the file ''%%checkp_file%%'' and after a while the computation stops. Restart it with

<code>
mpirun -np 8 ./build/Opt/bin/mptopcom -v -restart checkp_file < examples/cube_4.dat
</code>

===== Drawing the reverse search tree =====

''%%mptopcom1%%'' can output polymake code that one can paste into polymake to obtain the reverse search tree in the edge graph of the secondary polytope. This will not work for large examples, so handle with care. There are three possibilities:

  - Give ''%%mptopcom1%%'' an example without symmetry group:

<code>
./build/Opt/bin/mptopcom1 --make-tree < mp_examples/nosym/moae.dat
</code>

This will just draw all nodes in the same color and the edges between them that the reverse search used. 2. Give ''%%mptopcom1%%'' an example with symmetry group:

<code>
./build/Opt/bin/mptopcom1 --make-tree < examples/moae.dat
</code>

Now just the canonical representatives are drawn and the edges between them come from the reverse search, but they do not have to correspond to edges of the secondary polytope, since there can be a flip between classes of triangulations, while there is no flip between the canonical representatives. 3. Give ''%%mptopcom1%%'' an example with symmetry group and the parameter –make-marked-tree:

<code>
./build/Opt/bin/mptopcom1 --make-marked-tree  < examples/moae.dat
</code>

This call will make ''%%mptopcom1%%'' ignore the symmetry group. So the node number and the edges are the same as in 1. However, the tree generating procedure will use the symmetry group to color nodes according to their class membership.

===== Authors =====

**mptopcom** is joint work of the following three authors:

  * **[[https://www.otaru-uc.ac.jp/~skip/|Skip Jordan]]**, Department of Information and Management Science, Otaru University of Commerce, Japan
  * **[[https://page.math.tu-berlin.de/~joswig/|Michael Joswig]]**, Department of Mathematics, TU Berlin, Germany
  * **[[https://lkastner.github.io/|Lars Kastner]]**, Department of Mathematics, TU Berlin, Germany
  * **[[https://page.math.tu-berlin.de/~panizzut/|Marta Panizzut]]**, Department of Mathematics, TU Berlin, Germany

**mptopcom** is based on **TOPCOM** which is developed by

  * **[[https://www.rambau.wm.uni-bayreuth.de/|Jörg Rambau]]**, Department of Mathematics, Universität Bayreuth, Germany

===== Acknowledgements =====

We are very grateful to **[[https://www.math.tu-berlin.de/fachgebiete_ag_diskalg/fg_diskrete_mathematik_geometrie/v-menue/mitarbeiter/benjamin_lorenz/v-menue/home/|Benjamin Lorenz]]** for many discussions and for lending us his C++ expertise during the implementation phase.

===== License =====

**mptopcom** is licensed under the **[[https://www.gnu.org/licenses/gpl.html|GNU General Public License version 3]]**. **mptopcom** is based on **TOPCOM**, which is licensed under the **[[https://www.gnu.org/licenses/old-licenses/gpl-2.0.html|GNU General Public License version 2]]**, but allows redistributing its code under newer versions of the GPL. For configuring and installing **mptopcom** contains perl scripts from **polymake** that have been adapted to the setting of **mptopcom**. **polymake** is licensed under the **[[https://www.gnu.org/licenses/old-licenses/gpl-2.0.html|GNU General Public License version 2]]**, but allows redistributing its code under newer versions of the GPL.

See the files ''%%COPYING%%'' and ''%%LICENSE%%'' in the source for further details.