破坏发电机对称性
Breaking Generator Symmetry
摘要：
处理大量的对称性往往是有问题的。一个解决方案是只关注产生对称群的对称性。虽然有一些特殊的情况下，打破只是对称性在一个发电机组是完全的，也有情况下，没有非冗余发电机组消除所有的对称性。然而，只关注发电机可以提高可处理性。我们证明了消除所有对称解是多项式生成集的大小，但修剪所有对称值是NP-难的。我们的证明考虑了行和列对称性，这是矩阵模型中的一种常见对称类型，在这种模型中，打破生成器对称性非常有效。我们表明，传播的字典序约束矩阵的行和列的决策变量的连接是NP-难的。
英文摘要：
Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases where no irredundant generating set eliminates all symmetry. However, focusing on just generators improves tractability. We prove that it is polynomial in the size of the generating set to eliminate all symmetric solutions, but NP-hard to prune all symmetric values. Our proof considers row and column symmetry, a common type of symmetry in matrix models where breaking just generator symmetries is very effective. We show that propagating a conjunction of lexicographical ordering constraints on the rows and columns of a matrix of decision variables is NP-hard.
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