1. November 18, 2004 Energy Efficient Data Gathering in Sensor Networks F. Koushanfar, UCB N. Taft, Intel Research M. Potkonjak, UCLA A. Sangiovanni-Vincentelli, UCB Goals –Extend the lifetime of a network by reducing energy consuming activities such as sensing & communication. –Use a data-driven approach. Explore different energy saving approaches: –Sampling, Compression, Prediction & Sleeping –Consider these individually and jointly Methodology Non-parametric Statistical Modeling Sensor Data Learn Model Evaluate Sample Rate Selection Compression Inter-node Prediction ILP for Domatic Sets Sampling Rate Compressed Data Sleeping Schedule Sampling rate 1 in 2 (min) 1 in 5 (min) 1 in 10 (min) 1 in 20 (min) Temp (errors) 0001% Humidity (errors) 0001% Light (errors) 1%4%5%7% Why? Temporal correlation between signals is high Approach: –examine 1/m –use linear interpolation to predict unsampled points –select sampling rate based on a target error rate Take-away points –More reduction possible for temperature & humidity, less for light. –Different sensors have different minimal sampling rates Sampling 1/5 1/10 1/15 1/20 1/25 Sampling rate (30sec time unit) non-uniform sampling Small differences btwn successive samples more frequent than large differences => huffman coding attractive Results (percentage of bits needed) –Temperature 45%, Humidity 40%, Light 20% Take-away points –Light is most compressable modality –Savings uniform across all nodes –Huffman very close to optimal Compression Prediction Idea: take advantage of temporal and spatial correlations so that one node can be used to predict a few others. Approach: non-parametric method –Build histograms of conditional probabilities P(n2=y/n1=x) (pair-wise prediction) –Prediction: use average of this distribution (minimizes mean squared error) –Model Validation: resubstitution methods. Build model using 6 days, evaluate on next 21 days. Take-away points –For temperature & humidity, most nodes can be easily predicted by others to within 5% accuracy. –Light is more difficult to predict. –Prediction ability is often not symmetric. error rate frequency error rate n2 n1 n4 n5 n3n6 n7 e1P(n2|n1) e2P(n4|n1) : : e8P(n2|n5) Sleeping Coordination The weight of a directed edge ni  nj shows the conditional prob. P(nj|ni) Edges are included in the graph when probabilities are above a threshold Sample dominating sets n2 n1 n4 n5 n3n6 n7 e1 e2 e8 Avg. errorTempHumidityRuntime (seconds) 0.01110.04 0.02210.06 0.03520.09 0.04651.65 0.05963.70 Problem: Find the maximal number of disjoint dominating sets Can be formulated as an Integer Linear Program Take-away points –Short run times, optimal –Works well for temperature & humidity, but not for light –Works differently for differently modalities –If willing to tolerate 5% error rate in prediction, can extend lifetime 5-10 times –For light, it’s harder to find disjoint dominating sets Sleeping Coordination (Results ) Light Temperature Number of disjoint dominating sets for each value of error