## Maximizing the number of obnoxious facilities to locate within a bounded region.(English)Zbl 1171.90455

Summary: This paper deals with the problem of locating a maximal cardinality set of obnoxious facilities within a bounded rectangle in the plane such that their pairwise $$L_{\infty }$$-distance as well as the $$L_{\infty }$$-distance to a set of already placed demand sites is above a given threshold. We employ techniques and methods from computational geometry to design an optimization algorithm and an efficient $$\frac 1 2$$-approximation algorithm for the problem, and employ the optimization algorithm to design a PTAS based on the shifting strategy [D. S. Hochbaum and W. Maass, J. Assoc. Comput. Mach. 32, 130–136 (1985; Zbl 0633.68027)]. As a byproduct we improve the algorithm for placing obnoxious facilities given by M. Katz et al. [Improved algorithms for placing undesirable facilities. ibid. 29, 1859–72 (2002)].

### MSC:

 90B85 Continuous location

### Keywords:

abnoxious multifacility location; approximate solution

Zbl 0633.68027
Full Text:

### References:

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