Abstract
We show that the decision problem of determining whether a given (abstract simplicial) k-complex has a geometric embedding in Rd is complete for the Existential Theory of the Reals for all d≥3 and k∈{d−1,d}. This implies that the problem is polynomial time equivalent to determining whether a polynomial equation system has a real solution. Moreover, this implies NP-hardness and constitutes the first hardness results for the algorithmic problem of geometric embedding (abstract simplicial) complexes.
Original language | English |
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Publisher | arXiv |
Pages | 1-27 |
DOIs | |
Publication status | Published - 5 Nov 2021 |