On the asymptotic of the length of commercial traveller's path when towns are randomly allocated
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 828-831
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Let $n$ points in $R^k$ be independent and identically distributed. The paper is concerned with the well known problem of finding a cycle of minimal length that passes every point. Upper and lower bounds for the expectation of the length as $n\to\infty$ of this cycle are given. The bounds have equal growth rates. An algorithm is given to determine a cycle with average length between the bounds.
@article{TVP_1974_19_4_a11,
author = {L. Yu. Morosenzkii},
title = {On the asymptotic of the length of commercial traveller's path when towns are randomly allocated},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {828--831},
year = {1974},
volume = {19},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a11/}
}
TY - JOUR AU - L. Yu. Morosenzkii TI - On the asymptotic of the length of commercial traveller's path when towns are randomly allocated JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1974 SP - 828 EP - 831 VL - 19 IS - 4 UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a11/ LA - ru ID - TVP_1974_19_4_a11 ER -
L. Yu. Morosenzkii. On the asymptotic of the length of commercial traveller's path when towns are randomly allocated. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 828-831. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a11/