Paper by Erik D. Demaine

Reference:

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”, SIAM Journal on Computing, volume 35, number 3, 2005, pages 531–566.

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 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.

Comments:

This paper is also available from SIAM. This paper is also available as arXiv:cs.DS/0309014 of the Computing Research Repository (CoRR).

Length:

The paper is 36 pages.

Availability:

The paper is available in PDF (319k).

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SODA2001a (Optimal Covering Tours with Turn Costs)