1 Snapshot Queries: Towards Data- Centric Sensor Networks Yannis Kotidis AT&T Labs-Research ICDE 2005

2 Outline Introduction Overview Model Management Discovery of Representative Nodes Experiments

3 Introduction A lot of correlations exist in measurements between neighbors nodes. Only representative nodes reply the query Reduce the energy consumption Localized representative nodes selection algorithm Snapshot Node QUERY

4 Overview (1) Definitions of symbols ij Estimation

5 Overview (3) Each node N i contains  A fix-sized cache to store past measurements of neighbors.  Maintained by Model-aware Cache Management  A model to determine the correlations between neighbors.  Model x j as linear projection of x i : Node N i uses the model to produces an estimate of the measurement of its neighbor N j. Given an error metric d() and a threshold value T, node N i can represent N j if. ij represent estimate

6 Overview (4) Find representative relationship i k j [Model-Aware Cache Management] [Cache] Cache_line(N j ) = {(x i (1), x j (1)),…} Cache_line(N k ) = {(x i (3), x k (3)),…} x j (t) Node Ni reject keep Can N i represent N j ? Find optimal (a i.j, b i,j ) by LSE Representative

7 Overview (5) Find a small set of representative nodes Find the representative relationship Representative nodes Local Selection

8 Model Management (1) Modeling correlation  Given pairs of x i (t) and x j (t) : {(x i (t 1 ), x j (t 1 )),…,(x i (t n ), x j (t n ))}  Model x j (t) as linear projection of x i (t) :  Minimize the SSE :  Solve by least squares regression line:

9 Model Management (2) When new neighbor measurement x j is coming  Cache is not full  Insert to the cache line for N j  Cache is full  Time-shift the cache line for N j  Augment the cache line for N j  Reject the measurement pair i j [Cache] Cache_line(N j ) = {(x i (1), x j (1)),…} Cache_line(N k ) = {(x i (1), x k (1)),…} l x j (t) (x i (t),x j (t)) [Cache] Cache_line(N j ) = {(x i (1), x j (1)),…, (xi(t),xj(t))} Cache_line(N k ) = {(x i (1), x k (1)),…} drop

10 Model Management (3) Benefit of using the model for estimating in a cache line  For a cache line : c = { (x i (t 1 ), x j (t 1 )), (x i (t 2 ), x j (t 2 )), … }  The average SSE of model is :  The average SSE without model  The benefit of using model

11 Model Management (4) Cache line and estimation parameters  Current cache line :  Shifted cache line :  Augmented cache line :  a * (c), b * (c) is the optimal model parameters for of c Model-aware Cache Management 1. If  Reject the new pair (x i (t), x j (t)) 2. Else if  Time-shift the cache-line: c  c shift i j x j (t) (x i (t),x j (t)) When cache is full !!

12 Model Management (5)  If above 2 tests fail then Gains of augmenting cache line over time-shifted cache line Penalty of evicting oldest observation for another cache line c ’ of N k 3.1 If we can find for some k 3.2 If no such victim exists If  Time-shift Else  Reject the new measurement pair (x i (t), x j (t)) Cache_line(N j ) = {(x i (1), x j (1)), (x i (2),x j (2))…} Cache_line(N k ) = {(x i (1), x k (1)), (x i (3),x k (3))…} Cache_line(N l ) = {(x i (2), x l (2)), (x i (5),x l (5))…} Cache_line(N j ) = {(x i (1), x j (1)),…,(x i (t),x j (t))} Cache_line(N k ) = {(x i (1), x k (1)), (x i (3),x k (3)),…} Cache_line(N l ) = {(x i (5),x l (5)),…} Smallest Penalty augment drop

13 Discovery of Representative Nodes (1) The local policy for reducing the number of representatives is to have a node N j choose as its representative the node N i that can represent the larger number of nodes. Steps of local selection algorithm 1. Find the representative relationships 2. Initial selection of representatives 3. Refinement

14 Discovery of Representative Nodes (2) Initial selection of representative nodes Each node roadcast invitation message containing its current value x i (t) x 1 (t) x 4 (t) x 6 (t) 2. Each node broadcast its Cand_nodes i list 3. Each node select the node N j which can represent as its representative node, and N i ’s cand_nodes list is the longest. Send message to inform the selected representative node.

15 Discovery of Representative Nodes (3) Refinement Rule-0 Rule-2 Rule-3 Rule-2 Rule-3

16 Discovery of Representative Nodes (4) Messages number for representatives selection Each node sends 5 messages at most

17 Experiments Simulation Environment  Nodes Number N = 100  [0…1) x [0…1) two-dimensional area Simulation Data  Synthesized random walk data Nodes choose initial value in [0…1000] randomly Nodes are randomly partitioned to K classes Nodes in same class make a random step of the same direction (up or down) with a probability P move = [0.2…1]  Weather data Wind speed data from weather station of Washington University 100 series of 100-units data Average mean = 5.8, variance = 2.8

18 Experiments Sensitivity analysis  Synthesized random walk data  Data length = 100, Threshold T = 1, Measurement Pair Size = 8 byte  Broadcast first 10 data, and keep silent for next 90 data, and discover the representative nodes in the end. 1. Cache size R=√2, K=10 2. Transmission Range Cache Size = 2048 byte Stable

19 Experiments Savings during snapshot queries  Synthesized random walk data  200 queries, sink node for each queries was chosen randomly. N regular = participating nodes num for regular query W N snapshot = participating nodes num for snapshot query Saving Ratio = (N regular - N snapshot ) / (N regular ) increase

20 Experiments Experiments on weather data  Cache Size = 2048 bytes  Transmission Range = √2  Broadcast first 10 data, discover representatives nodes at the end. 0.1