Abstract
The shortest path tour problem (SPTP) consists in finding a shortest path from a given origination node s to a given destination node d in a directed graph with nonnegative arc lengths with the constraint that the optimal path P should successively and sequentially pass through at least one node from given node subsets T 1, T 2, . . . , T N , where \({T_i \cap T_j = \emptyset, \forall\ i, j=1,\ldots,N,\ i \neq j}\). In this paper, it will proved that the SPTP belongs to the complexity class P and several alternative techniques will be presented to solve it.
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Festa, P. Complexity analysis and optimization of the shortest path tour problem. Optim Lett 6, 163–175 (2012). https://doi.org/10.1007/s11590-010-0258-y
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DOI: https://doi.org/10.1007/s11590-010-0258-y