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.
A b s t r ac t . We report on the implementation of an algorithm for computing the set of all regular triangulations of finitely many points in Euclidean space. This algorithm, which we call down-flip reverse search, can be restricted, e.g., to computing full triangulations only; this case is particularly relevant for tropical geometry. Most importantly, down-flip reverse search allows for massive parallelization, i.e., it scales well even for many cores. Our implementation allows to compute the triangulations of much larger point sets than before.2010 Mathematics Subject Classification. 52B55 (68U05).
The QBF Gallery 2014 was a competitive evaluation for QBF solvers organized as part of the FLoC 2014 Olympic Games during the Vienna Summer of Logic. The QBF Gallery 2014 featured three different tracks on formulas in prenex conjunctive normal form (PCNF) including more than 1200 formulas to be solved. Gold, silver, and bronze track medals were awarded to the solvers that solved the most formulas in each of the three tracks. Additionally, the three participants that were most successful over the complete benchmark set were awarded with Kurt Gödel medals, the official prizes of the FLoC 2014 Olympic Games. In this paper, we give an overview of the setup and rules of the competition, briefly review the participating solvers, and finally report on the results of the QBF Gallery 2014.
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