| 释义 |
- References
- See also
The 1-center problem or minimax or minmax location problem is a classical combinatorial optimization problem in operations research of facilities location type. In its most general case the problem is stated as follows: given a set of n demand points, a space of feasible locations of a facility and a function to calculate the transportation cost between a facility and any demand point, find a location of the facility which minimizes the maximum facility-demand point transportation cost. There are numerous particular cases of the problem, depending on the choice of the locations both of demand points and facilities, as well as the distance function. A simple special case is when the feasible locations and demand points are in the plane with Euclidean distance as transportation cost (planar minmax Euclidean facility location problem, Euclidean 1-center problem in the plane, etc.). It is also known as the smallest circle problem. Its generalization to n-dimensional Euclidean spaces is known as the smallest enclosing ball problem. A further generalization (weighted Euclidean facility location) is when the set of weights is assigned to demand points and the transportation cost is the sum of the products of distances by the corresponding weights. Another special case, the closest string problem, arises when the inputs are strings and their distance is measured using Hamming distance. References- {{cite journal | last = Megiddo | first = Nimrod | title = The weighted Euclidean 1-center problem | journal = Mathematics of Operations Research | volume = 8 | issue = 4 | pages = 498–504 | publisher = Institute for Operations Research and the Management Sciences | location = Hanover (disambiguation) | date = November 1983 | url = http://theory.stanford.edu/~megiddo/pdf/weight1.pdf | doi=10.1287/moor.8.4.498}}
- {{cite journal | last = Foul | first = Abdelaziz | title = A 1-center problem on the plane with uniformly distributed demand points | journal = Operations Research Letters | volume = 34 | issue = 3 | pages = 264–268 | publisher = Elsevier | date = May 2006 | url = http://www.sciencedirect.com/science/article/pii/S016763770500060X | doi = 10.1016/j.orl.2005.04.011}}
- {{cite journal | last = Chandrasekaran | first = R. | title = The weighted euclidean 1-center problem | journal = Operations Research Letters | volume = 1 | issue = 3 | pages = 111–112 | publisher = Elsevier | date = July 1982 | url = http://www.sciencedirect.com/science/article/pii/0167637782900098 | doi = 10.1016/0167-6377(82)90009-8}}
- {{cite journal | last = Colebrook | first = M. |author2= J. Gutiérrez, S. Alonso|author3= J. Sicilia | title = A New Algorithm for the Undesirable 1-Center Problem on Networks | journal = Journal of the Operational Research Society | volume = 53 | issue = 12 | pages = 1357–1366 | publisher = Palgrave Macmillan Journals | date = December 2002 | jstor = 822725 | doi = 10.1057/palgrave.jors.2601468}}
- {{cite journal | last = Burkard | first = Rainer E. |author2= Helidon Dollani | title = A Note on the Robust 1-Center Problem on Trees | journal = Annals of Operations Research | volume = 110 | issue = 1–4 | pages = 69–82 | publisher = Kluwer Academic Publishers | date = February 2002 | issn = 1572-9338 | doi = 10.1023/A:1020711416254}}
See also- Minsum facility location (1-median problem), with geometric median being a special case
- Maxmin facility location (obnoxious facility location)
- k-center problem
- k-median problem
1 : Combinatorial optimization |