TY - JOUR

T1 - On the complexity of locating linear facilities in the plane

AU - Megiddo, Nimrod

AU - Tamir, Arie

N1 - 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,

PY - 1982/11

Y1 - 1982/11

N2 - 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.

AB - 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.

KW - NP-complete

KW - p-line center

KW - p-line median

KW - planar location

KW - strongly NP-complete

UR - http://www.scopus.com/inward/record.url?scp=0020202861&partnerID=8YFLogxK

U2 - 10.1016/0167-6377(82)90039-6

DO - 10.1016/0167-6377(82)90039-6

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AN - SCOPUS:0020202861

SN - 0167-6377

VL - 1

SP - 194

EP - 197

JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

ER -