Maximizing thenumberofobnoxiousfacilitiestolocatewithinaboundedregion

This paperdealswiththeproblemoflocatingamaximalcardinalitysetofobnoxiousfacilitieswithina bounded rectangleintheplanesuchthattheirpairwise L∞-distance aswellasthe L∞-distance toaset of alreadyplaceddemandsitesisaboveagiventhreshold.Weemploytechniquesandmethodsfrom computational geometrytodesignanoptimizationalgorithmandanefficient 12 -approximation algorithm for theproblem,andemploytheoptimizationalgorithmtodesignaPTASbasedontheshiftingstrategy [Hochbaum DS,MaassW.Approximationschemesforcoveringandpackingproblemsinimageprocessing and VLSI.JournaloftheACM1985;32:130–6].Asabyproductweimprovethealgorithmforplacing obnoxious facilitiesgivenbyKatzetal.[Improvedalgorithmsforplacingundesirablefacilities.Computers & OperationsResearch2002;29:1859–72.].