Ariel Rosenfeld 1. 2 1 0 1 1 1 0 1 0 0 1 1 Network Traffic Engineering. Call Record Analysis. Sensor...

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Ariel Rosenfeld 1 Slide 2 2 1 0 1 1 1 0 1 0 0 1 1 Network Traffic Engineering. Call Record Analysis. Sensor Data Analysis. Medical, Financial Monitoring. Etc, etc, etc. Slide 3 3 .1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 Time Increases Current Time Window Size = N Slide 4 Count the number of ones in N size window. Exact Solution: (N) memory. Approximate Solution: ? Good approx with o(N) memory? 4 Slide 5 Exponential Histogram (EH): 1 + approximation. (k = 1/) Space: O(1/(log 2 N)) bits. Time: O(log N) worst case, O(1) amortized. 5 Slide 6 6 Slide 7 7 Bucket sizes = 4,2,2,2,1.Bucket sizes = 4,4,2,1.Bucket sizes = 4,2,2,1,1,1.Bucket sizes = 4,2,2,1,1.Bucket sizes = 4,2,2,1. .1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 k/2 = 1. Element arrived this step. Future Slide 8 Error in last (leftmost) bucket. Bucket Sizes (left to right): C m,C m-1, ,C 2,C 1 Absolute Error = C m-1 ++C 2 +C 1 +1. Error