The growth of the size of the routing tables limits the scalability of the conventional IP routing. As scalable routing schemes for large-scale networks are highly demanded, this paper proposes and evaluates an efficient geometric routing scheme and related low-cost node design applicable to large-scale networks. The approach guarantees that greedy forwarding on derived coordinates will result in successful packet delivery to every destination in the network by relying on coordinates deduced from a spanning tree of the network. The efficiency of the proposed scheme is measured in terms of routing quality (stretch) and size of the coordinates. The cost of the proposed router is quantified in terms of area complexity of the hardware design and all the evaluations involve comparison with a state-of-the-art approach with virtual coordinates in the hyperbolic plane. Extensive simulations assess the proposal in large topologies consisting of up to 100K nodes. Experiments show that the scheme has stretch properties comparable to geometric routing in the hyperbolic plane, while enabling a more efficient hardware design, and scaling considerably better in terms of storage requirements for coordinate representation. These attractive properties make the scheme promising for routing in large networks.

The link structure of the Web is generally viewed as a webgraph. One of the main objectives of web structure mining is to find hidden communities on the Web based on the webgraph, and one of its approaches tries to enumerate substructures, each of which corresponds to a set of web pages of a community or its core. Research has shown that certain substructures can find sets of pages that are inherently irrelevant to communities. In this paper, we propose a model, which we call contracted webgraphs, where such substructures are contracted into single nodes to hide useless information. We then try structure mining iteratively on those contracted webgraphs since we can expect to find further hidden information once irrelevant information is eliminated. We also explore the structural properties of contracted webgraphs from the viewpoint of scale-freeness, and we observe that they exhibit novel and extreme self-similarities.

Recent studies investigating the Internet topology reported that inter Autonomous System (AS) topology exhibits a power-law degree distribution which is known as the scale-free property. Although there are many models to generate scale-free topologies, no game theoretic approaches have been proposed yet. In this paper, we propose the new dynamic game theoretic model for the AS level Internet topology formation. Through numerical simulations, we show our process tends to give emergence of the topologies which have the scale-free property especially in the case of large decay parameters and large random link costs. The significance of our study is summarized as following three topics. Firstly, we show that scale-free topologies can also emerge from the game theoretic model. Secondly, we propose the new dynamic process of the network formation game for modeling a process of AS topology formation, and show that our model is appropriate in the micro and macro senses. In the micro sense, our topology formation process is appropriate because this represents competitive and distributed situation observed in the real AS level Internet topology formation process. In the macro sense, some of statistical properties of emergent topologies from our process are similar to those of which also observed in the real AS level Internet topology. Finally, we demonstrate the numerical simulations of our process which is deterministic variation of dynamic process of network formation game with transfers. This is also the new result in the field of the game theory.