Dynamic Bi-Colored Graph Partitioning

Abstract

In this work, we focus on partitioning dynamic graphs with two types of nodes (bi-colored), though not necessarily bipartite graphs. They commonly appear in communication network applications, e.g., one color being base stations, the other users, and the dynamic process being the varying connection status between base stations and moving users. We introduce a partition cost function that incorporates the coloring of the graph and propose solutions based on the generalized eigenvalue problem (GEVP) for the static two-way partition problem. The static multi-way partition problem is then handled by a heuristic based on the two-way partition problem. Regarding the adaptive partition, an eigenvector update-based method is proposed. Numerical experiments demonstrate the performance of the devised approaches.