Suppose I have a directed graph, where it begins with a start node and ends with a end node. For each intermedia node, it has a type. There are directed edges defined in the nodes (not between every node pairs) with different distances. My problem is: how to find out a shortest path which ``passes each type of node for at least once''? Is it a well-known problem, or any kind of variants of travelling salesman problem?
2026-04-03 05:48:15.1775195295
Variants of travelling salesman problem: must visit each ``type'' of city for at least once.
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This variant is known as the Set TSP, as well as several other names mentioned in the link.
The first reference (Noon and Bean, 1993) describes a transformation in which each set/type is visited exactly once but mentions that Noon's dissertation [10] shows how to handle intraset arcs.