Mobile r-gather
Jiemin Zeng, Gaurish Telang, Matthew P. Johnson, Rik Sarkar, Jie Gao, Esther M. Arkin, Joseph S. B. Mitchell · 2017
We study the r-gather clustering problem in a mobile and distributed setting. In this problem, nodes must be clustered into groups of at least r nodes each, and the goal is to minimize the diameter of the clusters. This notion of clustering is motivated by protecting user anonymity in location-based services or trajectory publication. Prior works on r-gather problems are centralized and cannot be easily adapted to the mobile setting. We describe a distributed algorithm that produces compact clusters, within an approximation factor 4 of the minimum cluster diameter possible. The algorithm can run on the mobile nodes and access points at the network edge locally, and can handle node mobility, rapidly switching cluster memberships as needed. The distributed approach naturally comes with the advantage of greater resilience and stability. Additionally, we show that it achieves local optimality; i.e., from the point of view of any particular node, the solution is nearly as favorable as possible, irrespective of the global configuration. We also show how to cluster trajectories with dynamic re-groupings. Further, we improve the theoretical hardness results for the problem in the Euclidean setting.