Collective-k Optimal Location Selection

We study a novel location optimization problem, the Collective-k Optimal Location Selection (CkOLS) problem. This problem finds k regions such that setting up k service sites, one in each region, collectively attracts the maximum number of customers by proximity. The problem generalizes the traditional influence maximizing location selection problem from searching for one optimal region to k regions. This increases the complexity of the problem. We prove that the CkOLS problem is NP-hard, and propose both precise and approximate algorithms to solve this problem. The precise algorithm uses a brute-force search with a pruning strategy. The approximate algorithm adopts a clustering-based approach, which restricts the combinational search space within representative regions of clusters, and has a bounded approximation ratio. Extensive experiments show that the approximate algorithm is effective and efficient, and its output results are close to optimal.