We show that \textsc{number of bistellar moves and sparse degree-two edge collapses for 3-sphere} is NP-hard. It follows that a similar problem for an arbitrary 3-manifold is NP-hard as well. This is the first NP-hardness result concerning moves between two triangulations of a 3-manifold.

翻译：我们证明\textsc{三维球面的双星变换与稀疏度二边坍缩数量}问题是NP难的。由此可得，任意三维流形的类似问题也是NP难的。这是关于三维流形两三角剖分间移动的首个NP难度结果。