Scaling Bounds for Function Computation over Large Networks (Sundar Subramanian, Piyush Gupta, and Sanjay Shakkottai) : This paper essentially looked at the scaling laws for the “refresh rate” of networks in which a collector node wants to compute a function f(x1, x1, …, xn) of measurements at the nodes of a network. The network has bounded degree and there is a difference in scaling between type-sensitive (mean, mode) and type-threshold (max, min) functions. They show that deterministic bounds on type-sensitive functions are not possible in general, but probabilistic bounds are possible. By using a joint source-channel coding strategy, for AWGN networks they obtain constant refresh rates for small path-loss exponents.
Characterization of the Critical Density for Percolation in Random Geometric Graphs (Zhenning Kong and Edmund M. Yeh) : Since we had a reading group on percolation theory this semester, this talk felt right up my alley. Although using Monte Carlo techniques we know the critical threshold (density) for percolation (formation of a giant connected component) to happen in random geometric graphs, the analytical bounds are quite loose. This paper gets tighter analytical bounds by doing some smarter bounding of the “cluster coefficients,” which come from looking at the geometry of the percolation model.