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On The Approximability Of The Traveling Salesman Problem
Combinatorica, 2006We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than $$\frac{{117}}{{116}}$$ when the edge lengths are allowed to be asymmetric and $$\frac{{220}}{{219}}$$ when the edge lengths are symmetric, unless P=NP.
Christos H. Papadimitriou +1 more
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The greedy travelling salesman's problem
Networks, 1979AbstractThe Travelling Salesman's Problem is to find a Hamilton path (or circuit) which has minimum total weight W*, in a graph (or digraph) with a non‐negative weight on each edge. The Greedy Travelling Salesman's Problem is “How much larger than W* can the total weight G* of the solution obtained by the Greedy Algorithm be?”.
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On inverse traveling salesman problems
4OR, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yerim Chung, Marc Demange
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The clustered traveling salesman problem
Computers & Operations Research, 1975Abstract The traveling salesman problem is expanded to include the situation where a group of cities (cluster) must be visited contiguously in an optimal, unspecified order. Given several sets of clusters within the problem, a method is developed for optimizing simultaneously the ordering of cities within each cluster and the ordering of clusters.
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The hierarchical traveling salesman problem
Optimization Letters, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kiran Panchamgam +4 more
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Asparagos96 and the traveling salesman problem
Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97), 2002The paper describes a spatially structured evolutionary algorithm being applied to the symmetric and asymmetric traveling salesman problem (TSP). This approach shows that a genetic algorithm with high degree of isolation-by-distance in combination with a simple repairing mechanism is able to find high quality solutions for the TSP.
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Pyramidal traveling salesman problem
Computers & Operations Research, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Md. Fazle Baki, Santosh N. Kabadi
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Submodularity and the traveling salesman problem
European Journal of Operational Research, 1999Consider a central warehouse and a set \(V\) of retailers. For \(S \subseteq V\) let \(T(S)\) the length of an optimal traveling salesman tour through the retailers in \(S\) and the warehouse. The problem investigated is to find a submodular function \(K(S)\) and a small \(\alpha\) such that \(T(S)\leq K(S)\leq \alpha T(S)\) for all \(S\subseteq V ...
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Reoptimizing the traveling salesman problem
Networks, 2003AbstractIn this paper, we study the reoptimization problems which arise when a new node is added to an optimal solution of a traveling salesman problem (TSP) instance or when a node is removed. We show that both reoptimization problems are NP‐hard. Moreover, we show that, while the cheapest insertion heuristic has a tight worst‐case ratio equal to 2 ...
ARCHETTI, Claudia +2 more
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Maximum travelling salesman problem
Mathematical Methods of Operations Research, 1996Summary: We present different types of techniques for designing algorithms with worst-case performances for the Maximum Travelling Salesman Problem.
Vladimir Kotov, Michail M. Kovalev
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