Günter Rote:

The N-line traveling salesman problem

Networks 22 (1992), 91–108, (Zbl 783.90118, MR #92k:90045). doi:10.1002/net.3230220106

Abstract

We consider the special case of the Euclidean Traveling Salesman Problem where the given points lie on a small number (N) of parallel lines. Such problems arise for example in the fabrication of printed circuit boards, where the distance traveled by a laser which drills holes in certain places of the board should be minimized. By a dynamic programming algorithm, we can solve the N-line traveling salesman problem for n points in time nN, for fixed N, i. e., in polynomial time. This extends a result of Cutler (1980) for 3 lines. The parallelity condition can be relaxed to point sets which lie on N "almost parallel" line segments. We give a characterization of the allowed segment configurations by a set of forbidden subconfigurations.
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Erratum

The version that appears in Networks has an incorrect version of the corollary in Section 6, which characterizes the allowed segment configurations by forbidden subconfigurations: one case is missing in Figure 3. This is corrected in the technical report (see the links above), and in my dissertation, of which this paper is a part.

Last update: August 16, 2012.