Geodesic
Minimal weighted planar binary trees
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 375-409.

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The aim of the present work is to generalize the well known Melzak's algorithm and the notion of the twisting number to the case of weighted planar binary trees. That gives us the opportunity to obtain some essential restrictions to the possible topologies of minimal weighted planar binary trees. 
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     author = {A. O. Ivanov},
     title = {Minimal weighted planar binary trees},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {375--409},
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     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a2/}
}
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A. O. Ivanov. Minimal weighted planar binary trees. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 2, pp. 375-409. http://geodesic.mathdoc.fr/item/FPM_1996_2_2_a2/