Autonomous Decentralized Spectral Clustering for Hierarchical Routing of Multi-hop Wireless Networks

In multi-hop wireless networks (MWNs), hierarchical structures are important to achieve scalable routing control, as well as clustering algorithms for creating such structures and so have been extensively studied. Due to the constraints of MWNs as distributed systems, these clustering algorithms must be implemented in an autonomous and decentralized manner. In particular, ensuring transparency to network topology and node mobility is important. Spectral clustering is a technique for appropriately creating clusters regardless of the network topology. However, since this technique requires information on the entire network, it is difficult to implement it autonomously and in a decentralized manner. Therefore, autonomous and decentralized spectral clustering has only succeeded in simple grid networks. This paper proposes a spectral clustering algorithm that can be implemented in an autonomous and decentralized manner for any network topology. In this method, a certain spatial structure is generated in an autonomous and decentralized manner by using differential equation-based temporal evolution equations; clusters are then formed using the spatial structure yielded by the temporal evolution equations. We demonstrate that this method can realize spectral clustering in an autonomous and decentralized manner in a static network model and also can realize a stable cluster structure that responds to node movement in a dynamic network model.