Distance Preserving Graph Simplification

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph. Specifically, we construct a gate graph from a large graph so that for any "non-local" vertex pair (distance higher than some threshold) in the original graph, their shortest-path distance can be recovered by consecutive "local" walks through the gate vertices in the gate graph. We perform a theoretical investigation on the gate-vertex set discovery problem. We characterize its computational complexity and reveal the upper bound of minimum gate-vertex set using VC-dimension theory. We propose an efficient mining algorithm to discover a gate-vertex set with guaranteed logarithmic bound. We further present a fast technique for pruning redundant edges in a gate graph. The detailed experimental results using both real and synthetic graphs demonstrate the effectiveness and efficiency of our approach.Comment: A short version of this paper will be published for ICDM'11, December 201

Algorithms for the visualization and simulation of mobile ad hoc and cognitive networks

Visualization and simulation are important aspects of most advanced engineering endeavors. They may provide important insights into the functionality and perfor- mance of a system during the design and evaluation stage of the system's development. This thesis presents a number of algorithms and simulation algorithms that may be used for the design and evaluation of two types of engineered systems, mobile ad hoc and cognitive networks. The ¯rst set of algorithms provides signal radiation pattern and digital terrain visualization capabilities to OMAN, a mobile ad hoc network sim- ulator developed at Drexel University. The second set of algorithms provides a more general visualization capability for displaying complex graphs. These algorithms fo- cus on simplifying a complex graph in order to allow a user to explore its underlying basic structure. The thesis closes with a description of a GPU-based implementation of a set of spectrum-sensing algorithms. Spectrum sensing is an important function- ality needed for cognitive networks. The computational speed-ups provided by the GPU implementation o®er the possibility of real-time spectrum-sensing for adaptive, cognitive networks.M.S., Computer Science -- Drexel University, 200