Capacitated Kinetic Clustering in Mobile Networks by Optimal Transportation Theory

TL;DR

This paper introduces distributed, efficient algorithms for capacitated kinetic clustering in mobile networks, leveraging optimal transportation theory and power diagrams to adapt to mobility and improve computational speed.

Contribution

It develops a novel, scalable algorithm based on power diagrams for capacitated kinetic clustering, with analytical bounds on solution stability and significant speed improvements.

Findings

First analytical upper bound on solution changes due to mobility

Solution size proportional to number of base stations

Orders of magnitude faster than existing methods

Abstract

We consider the problem of capacitated kinetic clustering in which $n$ mobile terminals and $k$ base stations with respective operating capacities are given. The task is to assign the mobile terminals to the base stations such that the total squared distance from each terminal to its assigned base station is minimized and the capacity constraints are satisfied. This paper focuses on the development of \emph{distributed} and computationally efficient algorithms that adapt to the motion of both terminals and base stations. Suggested by the optimal transportation theory, we exploit the structural property of the optimal solution, which can be represented by a power diagram on the base stations such that the total usage of nodes within each power cell equals the capacity of the corresponding base station. We show by using the kinetic data structure framework the first analytical upper bound on the number of changes in the optimal solution, i.e., its stability. On the algorithm side, using the power diagram formulation we show that the solution can be represented in size proportional to the number of base stations and can be solved by an iterative, local algorithm. In particular, this algorithm can naturally exploit the continuity of motion and has orders of magnitude faster than existing solutions using min-cost matching and linear programming, and thus is able to handle large scale data under mobility.