2003/09/09 by Esther M. Arkin, Michael A. Bender, Arkin, Esther M. +10
Computer Science · Engineering · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #Optimization and Packing Problems #Robotic Path Planning Algorithms #cs.CG #cs.DS
paper · pdf · doi:10.48550/arxiv.cs/0309014
36 pages, 19 figures, 2 tables, Latex; to appear in SIAM Journal on Computing. New version contains more technical details in Sections 4.1, 5.1, 5.2, 5.5, four more figures, four more pages, as well as numerous smaller changes
openalex publication_date 2003/09/09 · arxiv created 2005/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 em 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.