Balanced location on a graph.

*(English)*Zbl 0874.90114Summary: The problem of locating service facilities with respect to a given set of demands on a graph is considered. The objective function to be minimized is equal to the maximum difference in the distance from a demand point to its farthest and nearest facility (balancing function). It is assumed that any facility has at most \(m\) possibilities for its location. For \(m=2\), the computational complexity of the problem is \(O(np^2\log p)\), where \(n\) is the number of demand points and \(p\) is the number of located facilities. For \(m>2\), the problem is NP-hard. Similar results are presented for boolean and strongly boolean versions of the problem.

##### MSC:

90B80 | Discrete location and assignment |

90C35 | Programming involving graphs or networks |

90C60 | Abstract computational complexity for mathematical programming problems |

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\textit{M. Gavalec} and \textit{O. Hudec}, Optimization 35, No. 4, 367--372 (1995; Zbl 0874.90114)

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##### References:

[1] | Gavalec, M. Computational Complexity of Consistent Choice Proceedings of the VI. Conference of EF TU. pp.70–74. Košice: Mathematical Section. |

[2] | Halpern I., Accord and Conflict Among Several Objectives in Locational Decisions on Tree Networks (1983) |

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[4] | Hansen P., An Algorithm for the Variance Point of a Network, RAIRO Rech. Oper 25 pp 119– (1991) · Zbl 0742.90048 |

[5] | Hudec O., Zeitsch. Oper. Res 36 pp 439– (1992) |

[6] | DOI: 10.1137/0405033 · Zbl 0825.68494 |

[7] | DOI: 10.1287/mnsc.29.4.482 · Zbl 0513.90022 |

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