2017
DOI: 10.1016/j.disopt.2017.08.005
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A linear time algorithm for the 3-neighbour Travelling Salesman Problem on a Halin graph and extensions

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Cited by 6 publications
(4 citation statements)
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“…Manyam et al propose several lower bounds for the Dubins multiple TSP. Woods et al study the k ‐neighbor TSP, which is an alternative modeling approach to find a flight tour of the minimum travel distance. Whereas in the classic TSP, the length of the tour is equal to the sum of edge lengths, in the k ‐neighbor TSP, the length also depends on the sequence of edges in this tour (see for a more precise definition).…”
Section: Planning Drone Operationsmentioning
confidence: 99%
“…Manyam et al propose several lower bounds for the Dubins multiple TSP. Woods et al study the k ‐neighbor TSP, which is an alternative modeling approach to find a flight tour of the minimum travel distance. Whereas in the classic TSP, the length of the tour is equal to the sum of edge lengths, in the k ‐neighbor TSP, the length also depends on the sequence of edges in this tour (see for a more precise definition).…”
Section: Planning Drone Operationsmentioning
confidence: 99%
“…It is easy to see that the standard TSP with distances d ij can be represented as a special case of QTSP with identical solution value by defining costs 1 2 (d ij + d jk ) for any transition from vertex i via j to k. Thus, the well-known fact that no constant-ratio approximation can exist for the TSP immediately carries over to the QTSP. For the special case of Halin graphs, it was shown in [31] that QTSP can be solved in linear time.…”
Section: Related Literaturementioning
confidence: 99%
“…In this problem, a Hamiltonian cycle in a complete directed graph has to be found such that the maximum sum of weights of m consecutive vertices is minimized. The class of MinMaxSum TSPs intersects with the Bottleneck TSP (Gilmore and Gomory [19], Burkard and Sandholzer [10], van der Veen [43], Burkard et al [9], Vairaktarakis [37,38], Kabadi and Punnen [25], LaRusic and Punnen [28]) and the TSP under Categorization (Punnen [33]), and it is also relevant to the k-Neighbor TSP (Woods et al [46]) and the Maximum Scatter TSP (Arkin et al [2], Chiang [12]).…”
Section: Literature Reviewmentioning
confidence: 99%