New variations of the reverse facility location problem

In this paper we consider a natural extension of the socalled reverse facility location problem which was introduced by Cabello et al. [3]. Given a set of n users and a set of m facilities, where a user takes service from its nearest facility, the objective is to place two new facilities such that the total number of users served by these two new facilities is maximized. We refer to this problem as the 2-MaxCov problem. In the L1 and L metrics, the worst case time and space complexities of our proposed algorithm for solving this problem are both O(n2 log n). In the L2 metric, if m = 1, the 2-MaxCov problem can be solved easily in O(n) time. We have also considered the obnoxious version of this problem, referred to as the 2-Farthest-MaxCov problem, where a user is served by its farthest facility. Our proposed algorithm for this problem runs in O(n log n) time for all the considered distance measures.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Bhaswar B. Bhattacharya, Subhas C. Nandy
• Keywords: 2-MaxCov Problem, CCCG 2010, Computational Geometry, Facility Location Problem, Log N