Speed-up Solving Linear Systems on Parallel Architectures via Aggregation of Clans (Dmitry Zaitsev, LVEE-2019)
Материал из 0x1.tv
- Дмитрий Зайцев
Varying minimal clan size brings in certain imbalance when solving a linear (Diophantine) system on parallel architectures via composition of its clans using open source software PaAd. The problem is partially mended by dynamic scheduling of jobs. The present paper studies a task of preliminary balancing the clan size via their aggregation represented as a special case of graph partitioning. Due to complexity of the optimization criteria, taking into consideration both the number of equations and the number of variables on two stages of solution — solving a system for each clan and solving a composition system — simplified variants of the task are considered and solved using heuristic techniques: a fast bin packing with the first fit on a sorted array algorithm and a multi-objective graph partitioning with software package METIS. Obtained benchmarks show that aggregation of clans brings in an additional 3 times speed-up.
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