We look at a model of random graphs suggested by Gilbert: given an integer n and δ > 0, scatter n vertices independently and uniformly on a metric space, and then add edges connecting pairs of vertices of distance less than δ apart. We consider the asymptotics...

In recent years the popularity of multi-hop wireless networks has been growing. Its flexible topology and abundant routing path enables many types of applications. However, the lack of a centralized controller often makes it difficult to design a reliable service in multi-hop wireless networks. While packet routing has been the center of attention for decades, recent research focuses on data discovery such as file sharing in multi-hop wireless networks. Although there are many peer-to-peer lookup (P2P-lookup) schemes for wired networks, they have inherent limitations for multi-hop wireless networks. First, a wired P2P-lookup builds a search structure on the overlay network and disregards the underlying topology. Second, the performance guarantee often relies on specific topology models such as random graphs, which do not apply to multi-hop wireless networks. Past studies on wireless P2P-lookup either combined existing solutions with known routing algorithms or proposed tree-based routing, which is prone to traffic congestion. In this paper, we present two wireless P2P-lookup schemes that strictly build a topology-dependent structure. We first propose the Ring Interval Graph Search (RIGS) that constructs a DHT only through direct connections between the

The exploration of quality clusters in complex networks is an important issue in many disciplines, which still remains a challenging task. Many graph clustering algorithms came into the field in the recent past but they were not giving satisfactory performance on the basis of robustness, optimality, etc. So, it is most difficult task to decide which one is giving more beneficial clustering results compared to others in case of real–world problems. In this paper, performance of RNSC (Restricted Neighbourhood Search Clustering) and MCL (Markov Clustering) algorithms are evaluated on a random geometric graph (RGG). RNSC uses stochastic local search method for clustering of a graph. RNSC algorithm tries to achieve optimal cost clustering by assigning some cost functions to the set of clusterings of a graph. Another standard clustering algorithm MCL is based on stochastic flow simulation model. RGG has conventionally been associated with areas such as statistical physics and hypothesis testing but have achieved new relevance with the advent of wireless ad-hoc and sensor networks. In this study, the performance testing of these methods is conducted on the basis of cost of clustering, cluster size, modularity index of clustering results and normalized mutual information (NMI) using both real and synthetic RGG.