Geodesic
Vector optimization of decompositions of root trees
Diskretnaya Matematika, Tome 3 (1991) no. 2, pp. 58-68 
A. A. Markov. Vector optimization of decompositions of root trees. Diskretnaya Matematika, Tome 3 (1991) no. 2, pp. 58-68. http://geodesic.mathdoc.fr/item/DM_1991_3_2_a3/
@article{DM_1991_3_2_a3,
     author = {A. A. Markov},
     title = {Vector optimization of decompositions of root trees},
     journal = {Diskretnaya Matematika},
     pages = {58--68},
     year = {1991},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1991_3_2_a3/}
}
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We consider the decompositions of root trees with vector vertex weights. We study a problem on the minimization of the number of the decomposition under a vector constraint. We prove the insolvability of this problem in a class of generalized finite automata over trees containing algorithms of gradient type. We estimate the error of the automaton algorithm, present an algorithm that solves a problem with polynomially bounded time complexity, and obtain an estimate for the number of parts of the decomposition.