组合对称的并行计算
Parallel Computation of Combinatorial Symmetries
摘要：
在实践中，组合结构的对称性是通过将结构转换成注释图来计算的，该注释图的自同构恰好对应于所需的对称性。一个自同构求解器，然后计算所构造的图的自同构群。这种求解器已经开发了50多年，并且可以使用高效的顺序单核工具。然而，没有竞争力的并行工具可用于该任务。我们介绍了一种新的并行随机算法，它是基于修改的个性化细化范式使用顺序求解器。随机化的使用至关重要地实现了平行化。我们报告了大量的基准测试结果，表明我们的求解器在单线程上与最先进的求解器相比具有竞争力，同时随着使用更多线程而扩展得非常好。这导致许多图形类的数量级改进超过了最先进的求解器。事实上，我们的工具是第一个并行图自同构工具，优于目前的顺序工具。
英文摘要：
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the automorphism group of the constructed graph. Such solvers have been developed for over 50 years, and highly efficient sequential, single core tools are available. However no competitive parallel tools are available for the task. We introduce a new parallel randomized algorithm that is based on a modification of the individualization-refinement paradigm used by sequential solvers. The use of randomization crucially enables parallelization. We report extensive benchmark results that show that our solver is competitive to state-of-the-art solvers on a single thread, while scaling remarkably well with the use of more threads. This results in order-of-magnitude improvements on many graph classes over state-of-the-art solvers. In fact, our tool is the first parallel graph automorphism tool that outperforms current sequential tools.
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