DATE: | Wednesday, September 6th |

TIME: | 12:00 PM - 1:00 PM |

PLACE: | McConnell 320 |

TITLE: | Extended Convex Hull |

SPEAKER: |
Komei Fukuda, Institute for Operations Research, Dept. of Mathematics, EPF-Lausanne, Switzerland. |

Consider the problem of computing a minimal H-representation of the convex hull of the union of k H-polytopes in R^d. We call this problem the extended convex hull or ECH for short.

Since the usual convex hull problem is a special case in which each H-polytope is a single point (representable as the intersection of d+1 halfspaces). Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto the two-dimensional space and solving a linear program. The resulting algorithm is polynomial in the sizes of input and output under the general position assumption.

(Joint work with T.M. Liebling and C. Lutolf.)

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