三角剖分中计数满足旋量的计算困难
Computational Hardness of Enumerating Satisfying Spin-Assignments in Triangulations
摘要：
满足表面三角剖分中的自旋指派是反铁磁伊辛模型在三角剖分上的最小能量状态，其对应于（通过几何对偶）立方无桥图中的完美匹配。在这项工作中，我们表明，它是NP-完全的决定是否表面三角承认一个令人满意的自旋分配，它是P-完全的，以确定这种分配的数量。这两个结果都是通过一个精心制作的（和非典型的）减少，映射到一个可定向的封闭曲面的三角剖分的3-合取范式的布尔公式。
英文摘要：
Satisfying spin-assignments in triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this work we show that it is NP-complete to decide whether or not a surface triangulation admits a satisfying spin-assignment, and that it is #P-complete to determine the number of such assignments. Both results are derived via an elaborate (and atypical) reduction that maps a Boolean formula in 3-conjunctive normal form into a triangulation of an orientable closed surface.
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