Algorithms for partitioning of large routing networks

Abstract

Partitioning of large networks is vital for decentralized management and control. This paper presents two algorithms called ‘Hierarchical Recursive Progression-1’ (HRP-1) and ‘Hierarchical Recursive Progression-2’ (HRP-2) for partitioning of large networks into subnetworks of limited size with very few interconnections between them. In other words, we are trying to maximize the internal nodes and minimize the external connections of the subnetworks. The restriction on the size and the external connections is obtained by comparison against a user-defined value for the size of the subnetwork and for external connections via a term called density. The density of a subnetwork is defined as the ratio of the number of external connections and the size of the subnetwork. The two algorithms presented in the paper are based on the principle of subnetwork clustering. At the start of the algorithms, the number of subnetworks is equal to the total number of nodes of the network with each subnetwork containing a single node. Later, subnetworks are merged at various runs of the algorithm to form new subnetworks using connectivity, density and size criteria. The algorithms terminate when all the subnetworks satisfy a user-defined size and density limit. The difference between the algorithms HRP-1 and HRP-2 lies in the definition of density of subnetworks and the way through which the subnetworks are grouped at consecutive iterations of the algorithm. Note that the number of nodes inside the subnetworks never violates the size limit, thereby ensuring even distribution of load on the partitions obtained. Finally, the two algorithms are compared and tested on randomly generated graphs and a part of Paris road Network.

Keywords:

• graph partitioning
• large networks
• distributed computing
• load balancing