Topology Discovery of Sparse Random Graphs With Few Participants

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is scheduled to appear in J. on Random Structures and Algorithm

An Abstraction Theory for Qualitative Models of Biological Systems

Multi-valued network models are an important qualitative modelling approach used widely by the biological community. In this paper we consider developing an abstraction theory for multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. This is important as it aids the analysis and comparison of multi-valued networks and in particular, helps address the well-known problem of state space explosion associated with such analysis. We also consider developing techniques for efficiently identifying abstractions and so provide a basis for the automation of this task. We illustrate the theory and techniques developed by investigating the identification of abstractions for two published MVN models of the lysis-lysogeny switch in the bacteriophage lambda.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Dynamic p-cycles selection in optical WDM Mesh networks

P-cycles have been recognized as a useful protection scheme in WDM mesh networks. This is a type of shared link protection that not only retains the mesh-like capacity efficiency, but also achieves the ring-like protection switching speed. However, finding the optimal set of p-cycles for protecting traffic demands is not a simple task and is an NP-hard problem. A general approach is to determine a set of candidate p-cycles and then determine optimal or near-optimal solutions by using integer linear programming (ILP) models or heuristics. In a dense mesh network, however, the number of candidate cycles is huge, and increases exponentially if the node number is increased. Thus, searching for a suitable set of efficient candidate cycles is crucial and imperative to balancing the computational time and the optimality of solutions. In this paper, we propose a dynamic P-cycles selection (DPS) algorithm that improves the efficiency of enumerating candidate p-cycles. The dynamic approach for cycle selection is based on the network state. In the DPS algorithm, all cycles are found and stored, then an efficient and sufficient set of p-cycles is extracted to achieve 100% working protection, minimize the spare capacity, and reduce time complexity

A knowledge-based system with learning for computer communication network design

Computer communication network design is well-known as complex and hard. For that reason, the most effective methods used to solve it are heuristic. Weaknesses of these techniques are listed and a new approach based on artificial intelligence for solving this problem is presented. This approach is particularly recommended for large packet switched communication networks, in the sense that it permits a high degree of reliability and offers a very flexible environment dealing with many relevant design parameters such as link cost, link capacity, and message delay