In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

—We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Âð1Þ time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Âð ffiffiffi n p Þ time units. We further extend our approach to a network with noisy links. While the refresh rate remains Âð1Þ time units per sample, the delay increases to Âð ffiffiffi n p log nÞ. The number of transmissions in both cases is ÂðnÞ per histogram sample. The achieved Âð1Þ refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Âð1= log nÞ for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate co...

• Type: Journal
• Year: 2011
• Where: TMC
• Authors: Srikanth K. Iyer, D. Manjunath, R. Sundaresan
• Keywords: Histogram, Refresh Rate, Time Units, TMC 2011