### Abstract

For every polynomial time algorithm which gives an upper bound {Mathematical expression}(K) and a lower bound vol(K) for the volume of a convex set K⊂R^{d}, the ratio {Mathematical expression}(K)/vol(K) is at least (cd/log d)^{d} for some convex set K⊂R^{d}.

Original language | English |
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Pages (from-to) | 319-326 |

Number of pages | 8 |

Journal | Discrete & Computational Geometry |

Volume | 2 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1987 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Discrete & Computational Geometry*,

*2*(1), 319-326. https://doi.org/10.1007/BF02187886

**Computing the volume is difficult.** / Bárány, Imre; Füredi, Z.

Research output: Contribution to journal › Article

*Discrete & Computational Geometry*, vol. 2, no. 1, pp. 319-326. https://doi.org/10.1007/BF02187886

}

TY - JOUR

T1 - Computing the volume is difficult

AU - Bárány, Imre

AU - Füredi, Z.

PY - 1987/12

Y1 - 1987/12

N2 - For every polynomial time algorithm which gives an upper bound {Mathematical expression}(K) and a lower bound vol(K) for the volume of a convex set K⊂Rd, the ratio {Mathematical expression}(K)/vol(K) is at least (cd/log d)d for some convex set K⊂Rd.

AB - For every polynomial time algorithm which gives an upper bound {Mathematical expression}(K) and a lower bound vol(K) for the volume of a convex set K⊂Rd, the ratio {Mathematical expression}(K)/vol(K) is at least (cd/log d)d for some convex set K⊂Rd.

UR - http://www.scopus.com/inward/record.url?scp=0000075710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000075710&partnerID=8YFLogxK

U2 - 10.1007/BF02187886

DO - 10.1007/BF02187886

M3 - Article

VL - 2

SP - 319

EP - 326

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -