A Framework for Evaluating the Performance of Cluster Algorithms for Hierarchical Networks

Table-driven routing algorithms in flat networks have the scalability problem due to the need for global topology updates. To reduce update cost, networks are hierarchically organized. Clustering algorithms organize flat networks into hierarchical networks. One important problem, which has not been adequately addressed so far, is to evaluate how good a clustering algorithm is. In other words, it is useful to know what the desired properties of hierarchical networks are. In this paper, we address this issue by considering the routing update cost, which can be measured by the total routing table size and the variance of cluster size distribution. We provide a set of desired properties of clustering algorithms. Applying these properties to the cluster structure generated by an algorithm, we can determine how good a clustering algorithm is. Specifically, we discuss how to choose appropriate number of hierarchy levels, number of clusters, and cluster size distribution, such that the topology update cost is minimized. The desired properties obtained from the analysis can be used as guidelines in the design of clustering algorithms for table-driven hierarchical networks. We apply the idea developed in this paper to evaluate three routing algorithms, namely the lowest ID algorithm, the maximum degree algorithm, and the variable degree clustering algorithm. We show how the variable degree clustering algorithm, which takes into account these desired properties, improves routing performance.