Taiwanese Journal of Mathematics


Tianran Chen, Tsung-Lin Lee, and Tien-Yien Li

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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.

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Taiwanese J. Math., Volume 18, Number 1 (2014), 93-114.

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

Primary: 52A39: Mixed volumes and related topics 65H10: Systems of equations 65H20: Global methods, including homotopy approaches [See also 58C30, 90C30] 90C05: Linear programming

mixed volume polyhedral homotopy parallel computing multi-core cluster


Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien. MIXED VOLUME COMPUTATION IN PARALLEL. Taiwanese J. Math. 18 (2014), no. 1, 93--114. doi:10.11650/tjm.18.2014.3276. https://projecteuclid.org/euclid.twjm/1499706333

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