Journal Article

FZJ-2019-00494

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Exact value for the average optimal cost of the bipartite traveling salesman and two-factor problems in two dimensions

Capelli, R. (Corresponding author)FZJ* ; Caracciolo, S. (Corresponding author) ; Di Gioacchino, A. (Corresponding author) ; Malatesta, E. M. (Corresponding author)

2018
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/21829  doi:10.1103/PhysRevE.98.030101

Abstract: We show that the average optimal cost for the traveling-salesman problem in two dimensions, which is the archetypal problem in combinatorial optimization, in the bipartite case, is simply related to the average optimal cost of the assignment problem with the same Euclidean, increasing, convex weights. In this way we extend a result already known in one dimension where exact solutions are avalaible. The recently determined average optimal cost for the assignment when the cost function is the square of the distance between the points provides therefore an exact prediction\overline{E_{N}} = \frac{1}{\pi} \log Nfor large number of points 2N. As a byproduct of our analysis also the loop covering problem has the same optimal average cost. We also explain why this result cannot be extended at higher dimensions. We numerically check the exact predictions.

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Contributing Institute(s):

1. Computational Biomedicine (IAS-5)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

Appears in the scientific report 2019

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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