Study of a Proposed Spectral-based Approach for Facility Location in Tree Topologies

The wide proliferation of smart devices in the emerging Internet of Things (IoT) networking environment necessitates a revisit to the facility location problems, i.e., where to locate a certain service facility in order to minimize a corresponding cost function (e.g., minimize energy consumption in wireless sensor network by selecting a suitable location for the sink). To address this problem for a single facility, a spectral-based approach is presented in this paper for tree topologies considering the principal eigenvector of the distance matrix and the aggregate traffic loads. It was observed using simulation that even for those cases that the proposed approach does not produce the optimal location (i.e., the solution of the median problem), the corresponding cost is still close to the minimum.