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The document (see pic. below) states that it is possible to find a cover of the plane by a subset of 3 half-planes. It proposes to use linear programming for this. How to formulate such a program?

enter image description here

The original document can be found here: On the Separation of a Polyhedron from Its Single-Part Mold.

EDIT: For clarity: i need to understand how can i use LP to find subcoverage of size 3 from coverage of bigger size.

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  • $\begingroup$ Have you looked at reference [10]? $\endgroup$ – Yuval Filmus Jul 2 '18 at 8:59
  • $\begingroup$ What document is your image taken from? You should give credit to the authors, and provide a link to the original. $\endgroup$ – Yuval Filmus Jul 2 '18 at 8:59
  • $\begingroup$ @YuvalFilmus looks like it is paywalled. $\endgroup$ – Yola Jul 2 '18 at 9:11
  • $\begingroup$ Sometimes there are free versions available on authors' websites. $\endgroup$ – Yuval Filmus Jul 2 '18 at 9:13
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    $\begingroup$ Can you explain what you already know, and what you are looking for? $\endgroup$ – Yuval Filmus Jul 2 '18 at 10:13
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I believe the connection between Helly's theorem and linear programming stems from this paper:

Amenta, Nina. "Helly-type theorems and generalized linear programming." Discrete & Computational Geometry 12, no. 3 (1994): 241-261. (Springer link.)

This arose from Nina Amenta's Ph.D. thesis (PDF download), under the direction of Raimund Seidel.

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  • $\begingroup$ thanks! very promising, hopefully i will have time to digest it. if i will find solution there i will accept your answer. $\endgroup$ – Yola Jul 2 '18 at 11:31

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