Efficient Algorithms for Obnoxious Facility Location on a Line Segment or Circle
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We study different restricted variations of the obnoxious facility location problem on a plane. The first is the constrained obnoxious facility location on a line segment (COFL-Line) problem. We provide an efficient algorithm for this problem that executes in O(n ^ 2 log k + n log k log (n^2 + k)) time. Our result improves on the best known result of O((nk)^2 log(nk) + (n + k) log (nk)) time obtained by Singireddy and Basappa<cit.>. We also study the same problem where the facilities must be placed on a given circle (the constrained obnoxious facility location on a circle (COFL-Circ) problem). We provide an efficient algorithm for this problem that executes in O(n ^ 2 log k + n log k log (n^2 + k)) time. Our result improves on the best known result of O((nk)^2 log(nk) + (n + k) log (nk)) time obtained by Singireddy and Basappa<cit.>. The third problem we study is the min-sum obnoxious facility location (MOFL) problem.We provide an efficient algorithm that executes in O(nk·α(nk) log^3 nk) time, where α(.) is the inverse Ackermann function. The best known previous result is an O(n^3k) time obtained by Singireddy and Basappa<cit.>.
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