Complexity indices for the traveling salesman problem based on short edge subgraphs

Dragoš Cvetković (), Mirjana Čangalović (), Zorica Dražić () and Vera Kovačević-Vujčić ()
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Dragoš Cvetković: Mathematical Institute SANU
Mirjana Čangalović: University of Belgrade
Zorica Dražić: University of Belgrade
Vera Kovačević-Vujčić: University of Belgrade

Central European Journal of Operations Research, 2018, vol. 26, issue 3, No 15, 759-769

Abstract: Abstract We present the extension of our previous work on complexity indices for the traveling salesman problem (TSP). Since we study the symmetric traveling salesman problem, the instances are represented by complete graphs G with distances between cities as the edge weights. A complexity index is an invariant of an instance I by which the execution time of an exact TSP algorithm for I can be predicted. We consider some subgraphs of G consisting of short edges and define several new invariants related to their connected components. For computational experiments we have used the well-known TSP Solver Concorde. Experiments with instances on 50 vertices with the uniform distribution of integer edge weights in the interval [1, 100] show that there exists a notable correlation between the sequences of selected invariants and the sequence of execution times of the TSP Solver Concorde. We provide logical explanations of these phenomena.

Keywords: Traveling salesman problem; Complexity index; Concorde TSP solver; Correlation (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10100-017-0513-8

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