Traversing a set of points with a minimum number of turns
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Traversing the machining graph
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Not being (super)thin or solid is hard: A study of grid Hamiltonicity
Computational Geometry: Theory and Applications
Reduction rules deliver efficient FPT-algorithms for covering points with lines
Journal of Experimental Algorithmics (JEA)
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Milling a graph with turn costs: a parameterized complexity perspective
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Computational Geometry: Theory and Applications
Experimental evaluation of algorithms for the orthogonal milling problem with turn costs
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Computational Geometry: Theory and Applications
Drawing hamiltonian cycles with no large angles
GD'09 Proceedings of the 17th international conference on Graph Drawing
On covering points with minimum turns
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Improved FPT algorithms for rectilinear k-links spanning path
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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We give the first algorithmic study of a class of "covering tour" problems related to the geometric traveling salesman problem: Find a polygonal tour for a cutter so that it sweeps out a specified region ("pocket") in order to minimize a cost that depends mainly on the number of turns. These problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems, as well as arc routing ("postman") problems with turn penalties. We prove the NP-completeness of minimum-turn milling and give efficient approximation algorithms for several natural versions of the problem, including a polynomial-time approximation scheme based on a novel adaptation of the $m$-guillotine method.