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- W2949368821 abstract "We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include begin{romannum} item[{}] {sc 3Sat, 1-3Sat, 1-Ex3Sat, Minimum Vertex Cover, Minimum Dominating Set, Minimum Feedback Vertex Set, X3C, Partition Into Triangles, and Clique Cover.} end{romannum} We also prove the {sf NP}-completeness of the {sc Ambiguous Satisfiability} problems cite{Sa80} and the {sf D$^P$}-completeness (with respect to random polynomial reducibility) of the unique satisfiability problems cite{VV85} associated with several of the above problems, when restricted to planar instances. Previously, very few {sf #P}-hardness results, no {sf NP}-hardness results, and no {sf D$^P$}-completeness results were known for counting problems, ambiguous satisfiability problems and unique satisfiability problems, respectively, when restricted to planar instances. Assuming {sf P $neq $ NP}, one corollary of the above results is There are no $epsilon$-approximation algorithms for the problems of maximizing or minimizing a linear objective function subject to a planar system of linear inequality constraints over the integers." @default.
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- W2949368821 date "1998-09-11" @default.
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- W2949368821 title "The Complexity of Planar Counting Problems" @default.
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