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An Effective Coreset Compression Algorithm for Large Scale Sensor Networks Dan Feldman, Andrew Sugaya Daniela Rus MIT. Data. Data. Data. Data. =. Data. Data. Data. How much data?. 1 GPS Packet = 100 bytes. (latitude, longitude, time). 1 GPS Packet = 100 bytes.

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**An Effective Coreset Compression Algorithm for Large Scale**Sensor NetworksDan Feldman, Andrew SugayaDaniela RusMIT**Data**Data Data Data = Data Data Data**1 GPS Packet**= 100 bytes (latitude, longitude, time)**1 GPS Packet**= 100 bytes every 10 seconds**~40 Mb / hour**or ~1 Gb / day**~1 Gb / day**per device**~300 million**smart phones sold in 2010 http://mobithinking.com/mobile-marketing-tools/latest-mobile-stats**For**100 million devices**For**100 million devices ~ 100 petabytes per day**~ 100 thousand**terabytes per day**GPS-points Data**• iPhones can collect high-frequency GPS traces • GPS-point = (latitude, longitude, time)**3-D Visualization**• axes: (latitude, longitude) • axis: time**Challenges**• Storing data on iPhone is expensive • Transmission data is expensive • Hard to interpret raw data • Dynamic real-time streaming data**Key Insight: Identify Critical Points**• Approximate the n points by k << n semantically meaningful connected segments**Our Approach**• Approximate the input GPS-points by connected segments using a k-spline • Output the text description of the endpoints (e.g., using Google Maps)**Solution overview**• Semantically compress data points • Use coresets • Fit lines to the semantic points • Use splines on coreset • Reverse geo-cite to get directions**Definition:-Spline**A -spline is a sequence of connected segments in**Distance to a Point**For:**Optimal -spline**• over every k-spline**Optimal -spline**• over every k-spline • is an optimal -splineof if :**Problem Statement**• Input: set P of n data points in Rd and integer k • Output: optimal k-spline for P that provides semantic compression for large data set P**Our Main Compression Theorem**• For every set of points in there is a subset C such that: • The maximum distance between a point in to its closest point in is at most • can be computed in time Example application • The optimal -spline of is an -approximation of • An -approximation for can be computed in time using time algorithm**Streaming Compression using merge & reduce**p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16**Parallel computation**p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16**Summary**-spline points

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