Mixed Volume Computation in Parallel

Efficient algorithms for computing mixed volumes, via the computation of mixed cells, have been implemented in DEMiCs [18] and MixedVol-2.0 [13]. While the approaches in those two packages are somewhat different, they follow the same theme and are both highly serial. To fit the need for the parallel computing, a reformulation of the algorithms is inevitable. This article proposes a reformulation of the algorithm for the mixed volume computation rooted from algorithms in graph theory, making it much more fine-grained and scalable. The resulting parallel algorithm can be readily adapted to both distributed and shared memory computing systems. Illustrated by the numerical results on several different architectures, the speedups of our parallel algorithms for the mixed volume computation are remarkable.