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mplrs: A scalable parallel vertex/facet enumeration code

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Abstract

We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the existing lrs code with only minor modifications. mplrs was derived from the earlier parallel implementation plrs, written by G. Roumanis in C\({++}\) which runs on a shared memory machine. By improving load balancing we are able to greatly improve performance for medium to large scale parallelization of lrs. We report computational results comparing parallel and sequential codes for vertex/facet enumeration problems for convex polyhedra. The problems chosen span the range from simple to highly degenerate polytopes. For most problems tested, the results clearly show the advantage of using the parallel implementation mplrs of the reverse search based code lrs, even when as few as 8 cores are available. For some problems almost linear speedup was observed up to 1200 cores, the largest number of cores tested. The software that was reviewed as part of this submission is included in lrslib-062.tar.gz which has MD5 hash be5da7b3b90cc2be628dcade90c5d1b9.

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Notes

  1. See posts for December 9, 2014 (Gurobi) and February 25, 2015 (CPLEX).

  2. John White prepared a long list of applications which is available at [6].

  3. http://cgm.cs.mcgill.ca/~avis/C/lrslib/lrslib.html.

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Acknowledgements

We thank Kazuki Yoshizoe for helpful discussions concerning the MPI library which improved mplrs ’ performance.

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Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto, Japan

    David Avis

  2. School of Computer Science, McGill University, Montréal, QC, Canada

    David Avis

  3. Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan

    Charles Jordan

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  1. David Avis
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Correspondence to Charles Jordan.

Additional information

This work was partially supported by JSPS Kakenhi Grants 16H02785, 23700019 and 15H00847, Grant-in-Aid for Scientific Research on Innovative Areas, ‘Exploring the Limits of Computation (ELC)’.

Appendix A: Code organization for mplrs

Appendix A: Code organization for mplrs

We give a brief outline of the code organization for mplrs v. 6.2. See the lrslib programmer’s guideFootnote 3 for additional information on the legacy lrslib code.

To begin, mplrs is built using the following files. Each file has a corresponding header file which we omit in this description.

  • lrslib.c legacy library code implementing reverse search for vertex/facet enumeration

  • Choice of arithmetic packages: (default) lrsgmp.c using the extended precision GNU MP library (libgmp), lrsmp.c the lrslib extended precision arithmetic package, or lrslong.c using fixed precision arithmetic (used in mplrs1)

  • mplrs.c MPI wrapper containing all parallelization code for mplrs

There are a number of other files used to build other lrslib components that are not used in mplrs; most relevant of these is the C\({++}\) parallel wrapper (plrs.cpp) used in plrs. Sample input files for mplrs can be found in the ine/ directory. See the programmer’s guide for more information on other files and details on the legacy lrslib code.

The mplrs code is split into three main functions: mplrs_master, mplrs_ worker, and mplrs_consumer which correspond to Algorithms 3, 4 and 5 respectively. The master sends work in the send_work function which calls the setparams function to set budgeting parameters as in Algorithm 3. The hook to lrslib code (BRS call in Algorithm 4) occurs in the do_work function. This is where actual work is performed.

The data structures particular to mplrs are defined in mplrs.h. Variables used only by the master are collected in the masterv data structure, which contains cobasis_list (L in Algorithm 3). Likewise, variables used only by the consumer are collected in the consumerv structure. Each process has an mplrsv structure. The mplrs.h file also contains definitions for the default values of all options.

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Avis, D., Jordan, C. mplrs: A scalable parallel vertex/facet enumeration code. Math. Prog. Comp. 10, 267–302 (2018). https://doi.org/10.1007/s12532-017-0129-y

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