We study a hard geometric problem. Given n points in the plane and a positive integer k, the Rectilinear k -Bends Traveling Salesman Problem asks if there is a piecewise linear tour through the n points with at most k bends where every line-segment in the path is either horizontal or vertical. The problem has applications in VLSI design. We prove that this problem belongs to the class FPT (fixed-parameter tractable). We give an algorithm that runs in O(kn 2+k 4k n) time by kernelization. We present two variations on the main result. These variations are derived from the distinction between line-segments and lines. Note that a rectilinear tour with k bends is a cover with k line-segments, and therefore a cover by lines. We derive FPT-algorithms using bounded-search-tree techniques and improve the time complexity for these variants. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Estivill-Castro, V., Heednacram, A., & Suraweera, F. (2010). The rectilinear K-bends TSP. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6196 LNCS, pp. 264–277). https://doi.org/10.1007/978-3-642-14031-0_30
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