Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 43 (2018) no. 1
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Dragoš Cvetković; Zorica Dražić; Vera Kovačević-Vujčić; Mirjana Čangalović. The traveling salesman problem: The spectral radius and the length of an optimal tour. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 43 (2018) no. 1. http://geodesic.mathdoc.fr/item/BASS_2018_43_1_a2/
@article{BASS_2018_43_1_a2,
author = {Drago\v{s} Cvetkovi\'c and Zorica Dra\v{z}i\'c and Vera Kova\v{c}evi\'c-Vuj\v{c}i\'c and Mirjana \v{C}angalovi\'c},
title = {The traveling salesman problem: {The} spectral radius and the length of an optimal tour},
journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
pages = {18 - 26},
year = {2018},
volume = {43},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BASS_2018_43_1_a2/}
}
TY - JOUR
AU - Dragoš Cvetković
AU - Zorica Dražić
AU - Vera Kovačević-Vujčić
AU - Mirjana Čangalović
TI - The traveling salesman problem: The spectral radius and the length of an optimal tour
JO - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY - 2018
SP - 18
EP - 26
VL - 43
IS - 1
UR - http://geodesic.mathdoc.fr/item/BASS_2018_43_1_a2/
ID - BASS_2018_43_1_a2
ER -
%0 Journal Article
%A Dragoš Cvetković
%A Zorica Dražić
%A Vera Kovačević-Vujčić
%A Mirjana Čangalović
%T The traveling salesman problem: The spectral radius and the length of an optimal tour
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2018
%P 18 - 26
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2018_43_1_a2/
%F BASS_2018_43_1_a2
We consider the symmetric traveling salesman problem $($TSP$)$ with instances represented by complete graphs with distances between cities as edge weights. Computational experiments with randomly generated instances on $50$ and $100$ vertices with the uniform distribution of integer edge weights in interval $[1,100]$ show that there exists a correlation between the sequences of the spectral radii of the distance matrices and the lengths of optimal tours obtained by the well known TSP solver Concorde. In this paper we give a partial theoretical explanation of this correlation.
