In this paper, we develop a formal framework for what a good community should look like and how strong a community is (community strength). One of the key innovations is to incorporate the concept of relative centrality into structural analysis of networks. In our framework, relative centrality is a measure that measures how important a set of nodes in a network is with respect to another set of nodes, and it is a generalization of centrality. Building on top of relative centrality, the community strength for a set of nodes is measured by the difference between its relative centrality with respect to itself and its centrality. A community is then a set of nodes with a nonnegative community strength. We show that our community strength is related to conductance that is commonly used for measuring the strength of a small community. We define the modularity for a partition of a network as the average community strength for a randomly selected node. Such a definition generalizes the original Newman's modularity and recovers the stability in as special cases. For the local community detection problem, we also develop efficient agglomerative algorithms that guarantee the community strength of the detected local community.

Abstract-An interactive video-on-demand (VoD) system allows users to access video services, such as movies, electronic encyclopedia, interactive games, and educational videos from video servers on a broadband network. This paper develops a performance evaluation tool for the system design. In particular, a user activity model is developed to describe the usage of system resources, i.e., network bandwidth and video server usage, by a user as it interacts with the service. In addition, we allow hatching of user requests, and the effect of such batching is captured in a batching model. Our proposed queueing model integrates both the user activity and the batching model. This model can be used to determine the requirements of network bandwidth and video server and, hence, the trade-off in communication and storage costs for different system resource configurations.

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Abstract-In this paper, we formulate an optimization problem for the design of light-tree based logical topology in Wavelength Division Multiplexing (WDM) networks. The problem is comprised of two parts: (1) multicast routing and wavelength assignment of light-trees, and (2) the design of light-tree based logical topology for multicast streams. In the first part, we use Mixed Integer Linear Programming (MILP) to solve the optimal routing and wavelength assignment problem of light-trees with an end-to-end delay bound, and obtain the optimal placement of power splitters and wavelength converters. The numerical results show that networks with just a few power splitters and wavelength converters can efficiently carry multicast data. In the second part, we extend the above formulation to design the logical topology based on light-trees for multicast streams. In our approach, a light-tree can carry data of multiple multicast streams, and data of a multicast stream may traverse multiple light-trees to reach a receiver. The numerical results show that our approach use network resources more efficiently, as compared to the approach with a separate light-tree for a multicast stream and to the approach of transporting multicast streams over lightpath based logical networks.

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