Geodesic
Realization of hypergraphs by trees of minimal diameter
Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 91-97.

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We suggest an algorithm of constructing a realization of a hypergraph $H=(VH,EH)$ by a tree of minimal diameter whose complexity is $$ O\Bigl(\max\Bigl(|VH|^3,|VH|\sum_{e_i\in EH} |e^i|^2\Bigr)\Bigr). $$ 
@article{DM_1997_9_2_a8,
     author = {O. I. Mel'nikov},
     title = {Realization of hypergraphs by trees of minimal diameter},
     journal = {Diskretnaya Matematika},
     pages = {91--97},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_2_a8/}
}
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O. I. Mel'nikov. Realization of hypergraphs by trees of minimal diameter. Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 91-97. http://geodesic.mathdoc.fr/item/DM_1997_9_2_a8/