On the complexity of locating linear facilities in the plane

Nimrod Megiddo*, Arie Tamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)194-197
Number of pages4
JournalOperations Research Letters
Volume1
Issue number5
DOIs
StatePublished - Nov 1982

Funding

FundersFunder number
National Science FoundationECS-8121741

    Keywords

    • NP-complete
    • p-line center
    • p-line median
    • planar location
    • strongly NP-complete

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