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About this paper

Heng Guo, Mark Jerrum

The authors prove that counting vertices of bounded 0/1 polytopes described by rational inequalities has no FPRAS unless RP = NP. They reduce counting graph homomorphisms to a four-state graph by constructing a polytope whose vertices correspond exactly to those maps. This establishes hardness for the general class, while hardness under totally unimodular constraints remains open.

Summary by alphaXiv.

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