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• W3033818404 abstract "We prove that the problem of deciding whether a two- or three-dimensional simplicial complex embeds into R 3 is NP -hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an S 3 filling is NP -hard. The former stands in contrast with the lower-dimensional cases, which can be solved in linear time, and the latter with a variety of computational problems in 3-manifold topology, for example, unknot or 3-sphere recognition, which are in NP ∩ co- NP. (Membership of the latter problem in co-NP assumes the Generalized Riemann Hypotheses.) Our reduction encodes a satisfiability instance into the embeddability problem of a 3-manifold with boundary tori, and relies extensively on techniques from low-dimensional topology, most importantly Dehn fillings of manifolds with boundary tori." @default.
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• W3033818404 date "2020-06-04" @default.
• W3033818404 modified "2023-10-18" @default.
• W3033818404 title "Embeddability in R ³ is NP-hard" @default.
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• W3033818404 doi "https://doi.org/10.1145/3396593" @default.
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