A note on the m-center problem with rectilinear distances.

*(English)*Zbl 0699.90028Summary: Given n demand points on a plane, the problem we consider is to locate a given number, m, of facilities on the plane so that the maximum of the set of rectilinear distances of each demand point to its nearest facility is minimized. This problem is known as the m-center problem on the plane. A related problem seeks to determine, for a given r, the minimum number of facilities and their locations so as to ensure that every point is within r units of rectilinear distance from its nearest facility. We formulate the latter problem as a problem of covering nodes by cliques of an intersection graph. Certain bounds are established on the size of the problem. An efficient algorithm is provided to generate this set-covering problem. Computational results with this approach are summarized.

##### MSC:

90B05 | Inventory, storage, reservoirs |

90C35 | Programming involving graphs or networks |

90C10 | Integer programming |

##### Keywords:

facility location; rectilinear distances; m-center problem; covering nodes by cliques; intersection graph
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\textit{Y. P. Aneja} et al., Eur. J. Oper. Res. 35, No. 1, 118--123 (1988; Zbl 0699.90028)

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