Complexity of Counting Weighted Eulerian Orientations with ARS

04/04/2019

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by   Jin-Yi Cai, et al.

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Unique prime factorization of integers is taught in every high school. We define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian orientation problems with arrow reversal symmetry (ARS). We establish a novel connection between counting constraint satisfaction problems and counting weighted Eulerian orientation problems that is global in nature, and is based on the determination of half-weighted affine linear subspaces.