FROST: Movement History-Conscious Facility Relocation.

The facility relocation (FR) problem, which aims to optimize the placement of facilities to accommodate the changes of users’ locations, has a broad spectrum of applications. Despite the significant progress made by existing solutions to the FR problem, they all assume each user is stationary and represented as a single point. Unfortunately, in reality, objects (e.g., people, animals) are mobile. For example, a car-sharing user picks up a vehicle from a station close to where he or she is currently located. Consequently, these efforts may fail to identify a superior solution to the FR problem. In this article, for the first time, we take into account the movement history of users and introduce a novel FR problem, called motion-fr, to address the preceding limitation. Specifically, we present a framework called frost to address it. frost comprises two exact algorithms: index based and index free. The former is designed to address the scenario when facilities and objects are known a priori, whereas the latter solves the motion-fr problem by jettisoning this assumption. Further, we extend the index-based algorithm to solve the general k-motion-fr problem, which aims to relocate k inferior facilities. We devise an approximate solution due to NP-hardness of the problem. Experimental study over both real-world and synthetic datasets demonstrates the superiority of our framework in comparison to state-of-the-art FR techniques in efficiency and effectiveness.