论文标题
通过不变的增强异态模型过滤
Boosting Isomorphic Model Filtering with Invariants
论文作者
论文摘要
有限模型的枚举对于工作离散数学家（代数，图理论等）非常重要，因此寻找有效的方法来完成此任务是离散计算数学的关键目标。但是，许多同构模型的可能存在，通常只会增加噪声。通常，它们被过滤掉{\ em a后验}，这一步骤可能需要很长时间才能丢弃冗余模型。本文提出了一种新的方法，将生成的模型分为相互非同构块。为此，我们使用精心设计的手工制作的不变性以及随机生成的不变性。然后将块分别且可能平行处理。这种方法被整合到MACE4（数学家中最受欢迎的工具）中，它显示了各种代数结构的巨大加速。
The enumeration of finite models is very important to the working discrete mathematician (algebra, graph theory, etc) and hence the search for effective methods to do this task is a critical goal in discrete computational mathematics. However, it is hindered by the possible existence of many isomorphic models, which usually only add noise. Typically, they are filtered out {\em a posteriori}, a step that might take a long time just to discard redundant models. This paper proposes a novel approach to split the generated models into mutually non-isomorphic blocks. To do that we use well-designed hand-crafted invariants as well as randomly generated invariants. The blocks are then tackled separately and possibly in parallel. This approach is integrated into Mace4 (the most popular tool among mathematicians) where it shows tremendous speed-ups for a large variety of algebraic structures.
