The lawnmower problem and other geometric path covering problems
We discuss the Lawnmower Problem: Given a polygonal region, find the shortest closed path along which we have to move a given object (typically a square or a circle), such that any point of the region will be covered by the object for some position of it movement. In another version of the problem, known as the Milling Problem, the object has to stay within the region at all times. Practical motivations for considering the Lawnmower Problem come from manufacturing (spray painting, quality control), geography (aerial surveys), optimization (tour planning for a large number of clients with limited mobility), and gardening. The Milling Problem has gained attention by its importance for NC pocket machining. We show that both problems are NP-hard and discuss approximation methods for various versions of the problem.
- OSTI ID:
- 35997
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0265
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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