In combinatorial optimization, the set TSP, also known as the, generalized TSP, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the Traveling salesman problem (TSP), whereby it is required to find a shortest tour in a graph which visits all specified disjoint subsets of the vertices of a graph. The ordinary TSP is a special case of the set TSP when all subsets to be visited are singletons. Therefore the set TSP is also NP-hard.
There is a direct reduction from set TSP to asymmetric TSP, and thus from set TSP to TSP. The idea is to arbitrarily assign a directed cycle to each set. The salesman, when visiting a vertex in some set, then walks around the cycle for free. To not use the cycle would ultimately be very costly.
Famous quotes containing the words problem and/or set:
“The general public is easy. You don’t have to answer to anyone; and as long as you follow the rules of your profession, you needn’t worry about the consequences. But the problem with the powerful and rich is that when they are sick, they really want their doctors to cure them.”
—Molière [Jean Baptiste Poquelin] (1622–1673)
“Through dinner she felt a gradual icy coldness stealing through her like novocaine. She had made up her mind. It seemed as if she had set the photograph of herself in her own place, forever frozen into a single gesture.”
—John Dos Passos (1896–1970)