Paper by Erik D. Demaine

Esther M. Arkin, Michael A. Bender, Erik D. Demaine, Sándor P. Fekete, Joseph S. B. Mitchell, and Saurabh Sethia, “Optimal Covering Tours with Turn Costs”, in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington, DC, January 7–9, 2001, pages 138–147.

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 not only on the length of the tour but also 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 lower bounds (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.

The paper is 10 pages.

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Related papers:
Milling (Optimal Covering Tours with Turn Costs)

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Last updated March 12, 2024 by Erik Demaine.