Shortest rectilinear paths among weighted obstacles
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
Rectilinear paths among rectilinear obstacles
Discrete Applied Mathematics
Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Information Processing Letters
Optimal Covering Tours with Turn Costs
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
An O(n5/2logn) algorithm for the Rectilinear Minimum Link-Distance Problem in three dimensions
Computational Geometry: Theory and Applications
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We study a hard geometric problem. Given n points in the plane and a positive integer k, the RECTILINEAR k-BENDS TRAVELLING 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 (fixedparameter tractable). We give an algorithm that runs in O(kn2 + k4kn) 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