@article{204ea460ff014dfbb32286389f15f7b3,
title = "On the complexity of locating linear facilities in the plane",
abstract = "We consider the computational complexity of linear facility location problems in the plane, i.e., given n demand points, one wishes to find r lines so as to minimize a certain objective-function reflecting the need of the points to be close to the lines. It is shown that it is NP-hard to find r lines so as to minimize any isotone function of the distances between given points and their respective nearest lines. The proofs establish NP-hardness in the strong sense. The results also apply to the situation where the demand is represented by r lines and the facilities by n single points.",
keywords = "NP-complete, p-line center, p-line median, planar location, strongly NP-complete",
author = "Nimrod Megiddo and Arie Tamir",
note = "Funding Information: * The first author was supported in part by the National Science Foundation under Grant ECS-8121741. ** Cummtly visiting at Carnegie-Mellon University, Graduate School of Industrial Adm~ini_stration,P ittsburgh, PA 15213,",
year = "1982",
month = nov,
doi = "10.1016/0167-6377(82)90039-6",
language = "אנגלית",
volume = "1",
pages = "194--197",
journal = "Operations Research Letters",
issn = "0167-6377",
publisher = "Elsevier B.V.",
number = "5",
}