Optimal Covering Tours with Turn Costs
Abstract
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 NPcompleteness of minimumturn milling and give efficient approximation algorithms for several natural versions of the problem, including a polynomialtime approximation scheme based on a novel adaptation of the mguillotine method.
 Publication:

arXiv eprints
 Pub Date:
 September 2003
 arXiv:
 arXiv:cs/0309014
 Bibcode:
 2003cs........9014A
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Geometry;
 F.2.2
 EPrint:
 36 pages, 19 figures, 2 tables, Latex