In this chapter, we will give a PTAS for the special case of the traveling salesman problem in which the points are given in a d-dimensional Euclidean space. As before, the central idea of the PTAS is to define a “coarse solution”, depending on the error parameter ε, and to find it using dynamic programming. A feature this time is that we do not know a deterministic way of specifying the coarse solution — it is specified probabilistically.
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