Embedding Divisor and Semi-Prime Testability in f-Vectors of Polytopes

Eran Nevo

doi:10.1007/s00454-022-00448-y

Embedding Divisor and Semi-Prime Testability in f-Vectors of Polytopes

Eran Nevo

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	297-303
Number of pages	7
Journal	Discrete and Computational Geometry
Volume	70
Issue number	1
DOIs	https://doi.org/10.1007/s00454-022-00448-y
State	Published - 1 Jul 2023
Externally published	Yes

Keywords

Computational complexity
Polytopes
f-vector

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-022-00448-y

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abstract = "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.",

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AB - 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.

KW - Computational complexity

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Embedding Divisor and Semi-Prime Testability in f-Vectors of Polytopes

Abstract

Keywords

ASJC Scopus subject areas

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