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تسجيل مستخدم جديدThe Asymmetric Traveling Salesman Problem on Graphs with Bounded Genus
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نشر من قبل
Shayan Oveis Gharan
تاريخ النشر
2009
مجال البحث
الهندسة المعلوماتية
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English
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We give a constant factor approximation algorithm for the asymmetric traveling salesman problem when the support graph of the solution of the Held-Karp linear programming relaxation has bounded orientable genus.
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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, Mk{a}dry, 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.
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A new characterisation of Hamiltonian graphs using f-cutset matrix is proposed. A new exact polynomial time algorithm for the travelling salesman problem (TSP) based on this new characterisation is developed. We then define so called ordered weighted
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