We obtain computational hardness results for f-vectors of polytopes by exhibiting reductions of the problems DIVISOR and SEMI-PRIME TESTABILITY to problems on f-vectors of polytopes. Further, we show that the corresponding problems for f-vectors of simplicial polytopes are polytime solvable. The situation where we prove this computational difference (conditioned on standard conjectures on the density of primes and on P≠ NP) is when the dimension d tends to infinity and the number of facets is linear in d.
Bibliographical notePublisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Computational complexity