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  1. Learning network topology from partial knowledge of its connectivity is an important objective in practical scenarios of communication networks and social-media networks. Representing such networks as connected graphs, exploring and recovering connectivity information between network nodes can help visualize the network topology and improve network utility. This work considers the use of simple hop distance measurement obtained from a fraction of anchor/source nodes to reconstruct the node connectivity relationship for large scale networks of unknown connection topology. Our proposed approach consists of two steps. We first develop a tree-based search strategy to determine constraints on unknown network edges based on the hop count measurements. We then derive the logical distance between nodes based on principal component analysis (PCA) of the measurement matrix and propose a binary hypothesis test for each unknown edge. The proposed algorithm can effectively improve both the accuracy of connectivity detection and the successful delivery rate in data routing applications. 
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  2. Auction-based service provisioning and resource allocation have demonstrated strong potential in Cloud-RAN wireless network architecture and heterogeneous networks for effective resource sharing. One major technical challenge is the integration of interference constraints in auction-based solutions. In this work we transform the interference constraint requirement into a set of linear constraints on each cluster. We tackle the generally NP-hard clustering problem by developing a novel practical suboptimal solution that can meet our design requirement. Our novel algorithm utilizes the properties of chordal graphs and applies Lexicographic Breadth First Search (Lex-BFS) algorithm for cluster splitting. This polynomial time approximate algorithm searches for maximal cliques in a graph by generating strong performance in terms of subgraph density and probability of optimal clustering without suffering from the high complexity of the optimal solution. 
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