scholarly journals A Constant-factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem

2020 ◽  
Vol 67 (6) ◽  
pp. 1-53
Author(s):  
Ola Svensson ◽  
Jakub Tarnawski ◽  
László A. Végh
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Constant Factor ◽  
Traveling Salesman ◽  
Asymmetric Traveling Salesman Problem

scholarly journals Approximation Algorithms for the Bottleneck Asymmetric Traveling Salesman Problem

2021 ◽  
Vol 17 (4) ◽  
pp. 1-12
Author(s):  
Hyung-Chan An ◽  
Robert Kleinberg ◽  
David B. Shmoys
Keyword(s):  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Related Result ◽  
Traveling Salesman ◽  
Performance Guarantee ◽  
Asymmetric Traveling Salesman Problem ◽  
Algorithmic Technique ◽  
Edge Cost

We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem . Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-length edge) cost. We achieve an O (log n / log log n ) approximation performance guarantee by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed. This allows us to build on a related result of Asadpour, Goemans, Mądry, Oveis Gharan, and Saberi to obtain this guarantee. Furthermore, we show how our technique yields stronger approximation bounds in some cases, such as the bounded orientable genus case studied by Oveis Gharan and Saberi. We also explore the possibility of further improvement upon our main result through a comparison to the symmetric counterpart of the problem.

AnO(logn/log logn)-Approximation Algorithm for the Asymmetric Traveling Salesman Problem

2017 ◽  
Vol 65 (4) ◽  
pp. 1043-1061 ◽  
Author(s):  
Arash Asadpour ◽  
Michel X. Goemans ◽  
Aleksander Mądry ◽  
Shayan Oveis Gharan ◽  
Amin Saberi
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Asymmetric Traveling Salesman Problem

scholarly journals Comparison of the Sub-Tour Elimination Methods for the Asymmetric Traveling Salesman Problem Applying the SECA Method

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Ramin Bazrafshan ◽  
Sarfaraz Hashemkhani Hashemkhani Zolfani ◽  
S. Mohammad J. Mirzapour Al-e-hashem
Keyword(s):  
Traveling Salesman Problem ◽  
Mathematical Problem ◽  
Multiple Criteria Decision Making ◽  
Traveling Salesman ◽  
Mathematical Problem Solving ◽  
Web Based ◽  
Asymmetric Traveling Salesman Problem ◽  
Simultaneous Evaluation ◽  
Mcdm Method ◽  
The Traveling Salesman Problem

There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results.

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