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.
Keywords:
Traveling salesman problem / Spectra of graphs / Spectral radius / Concorde TSP solver
Source:
Bulletin T.CLI de l’Académie serbe des sciences et des arts, 2018, 17-26
TY - CONF
AU - Cvetković, Dragoš
AU - Dražić, Zorica
AU - Kovačević-Vujčić, Vera
AU - Čangalović, Mirjana
PY - 2018
UR - https://dais.sanu.ac.rs/123456789/9081
AB - 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.
PB - Beograd : Académie Serbe des sciences et des arts
C3 - Bulletin T.CLI de l’Académie serbe des sciences et des arts
T1 - The traveling salesman problem: The spectral radius and the length of an optimal tour
SP - 17
EP - 26
UR - https://hdl.handle.net/21.15107/rcub_dais_9081
ER -
@conference{
author = "Cvetković, Dragoš and Dražić, Zorica and Kovačević-Vujčić, Vera and Čangalović, Mirjana",
year = "2018",
abstract = "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.",
publisher = "Beograd : Académie Serbe des sciences et des arts",
journal = "Bulletin T.CLI de l’Académie serbe des sciences et des arts",
title = "The traveling salesman problem: The spectral radius and the length of an optimal tour",
pages = "17-26",
url = "https://hdl.handle.net/21.15107/rcub_dais_9081"
}
Cvetković, D., Dražić, Z., Kovačević-Vujčić, V.,& Čangalović, M.. (2018). The traveling salesman problem: The spectral radius and the length of an optimal tour. in Bulletin T.CLI de l’Académie serbe des sciences et des arts
Beograd : Académie Serbe des sciences et des arts., 17-26.
https://hdl.handle.net/21.15107/rcub_dais_9081
Cvetković D, Dražić Z, Kovačević-Vujčić V, Čangalović M. The traveling salesman problem: The spectral radius and the length of an optimal tour. in Bulletin T.CLI de l’Académie serbe des sciences et des arts. 2018;:17-26.
https://hdl.handle.net/21.15107/rcub_dais_9081 .
Cvetković, Dragoš, Dražić, Zorica, Kovačević-Vujčić, Vera, Čangalović, Mirjana, "The traveling salesman problem: The spectral radius and the length of an optimal tour" in Bulletin T.CLI de l’Académie serbe des sciences et des arts (2018):17-26,
https://hdl.handle.net/21.15107/rcub_dais_9081 .
