DSI : A Fully Distributed Spatial Index for Location-based Wireless Broadcast Services Sungwon Jung Dept. of Computer Science and Engineering Sogang University Seoul, Korea

Motivation of DSI 2  Motivation  To supports location-based services in wireless data broadcast systems  To address inherited deficiencies of tree indexes Problem1. Must wait for the arrival of the root node Problem2. The search has to be stopped if index node is lost

Index Structure of DSI 3  Basic Idea  Divide the whole set of data objects into n f frames and associate with each frame an index table  The number of frames covered is exponentially increased with the order of index table entries ( R i th to R i+1 -1th ) A Broadcast Cycle n F = 8 i = th 2 1 th 2 2 th HC i PiPi smallest HC value of the object within frame point to the next r i th frame Index base(r) = 2 # of index table entries = log r n F = log 2 8 = 3 0 ≤ i ≤ (log r n F )-1  0 ≤ i ≤ 2 Index base(r) = 2 # of index table entries = log r n F = log 2 8 = 3 0 ≤ i ≤ (log r n F )-1  0 ≤ i ≤ 2

Energy Efficient Forwarding(1) 4  EEF is  Efficiently reach a frame containing the data object of a given location  Steps of EEF (given a target point, p)  Compute the HC value of p, ( HC p )  Tunes into the broadcast channel (Initial probe)  Comparing HC p with HC i maintained in the index table  Client follows the pointer P i, where

Energy Efficient Forwarding(2) 5  Example (find O 51 )  HC p = 51 O6O6 O 11 O 17 O 27 O 32 O 40 O 51 O 61 O6O6 O 11 O 17 O 27 Initial Probe HC 0 HC 1 HC HC 0 HC 1 HC 2 Active mode Doze mode Stop Searching F1F2F3F4F5F6F7F8

Window Queries(1) 6  Window query  returns all the data objects associated with locations within a given query window W  Steps of Window query  Detects all the intersections between the HC and W Target segment H = [10,11] [28,35] [52,53] Target segment H = [10,11] [28,35] [52,53]

Window Queries(2) 7  Window query  returns all the data objects associated with locations within a given query window W  Steps of Window query  Client scans each entry and follows the pointer P i with the range overlapping with segment of H Target segment H = [10,11] [28,35] [52,53] Target segment H = [10,11] [28,35] [52,53] Target segment H = [28,35] [52,53] Target segment H = [28,35] [52,53] Target segment H = [52,53] Target segment H = [52,53] Target segment H = [ ] Target segment H = [ ]

K-NN Queries(1) 8  Basic Idea  To determine a search space based on the partial knowledge of object distribution obtained from index  Search space will continuously shrink as more knowledge of the data distribution is obtained  Properties  Initial search space  whole spatial region  draw a circle centered at query point p, include at least k data objects  How to determine the search space Conservative Approach Aggressive Approach

K-NN Queries(2) 9  Conservative Approach  Retrieves a data object if it may potentially be in the answer set  Have small access latency but high energy expense ex. k = 3, a given query point p = 33. kNN = {6, 11, 32} from O 6 index frame kNN = {27, 32, 40} from O 11 index frame Ignore O 11 and Skip F 3 (O 17 ) kNN = {27, 32, 40} from O 27 index frame kNN = {32, 40, 51} from O 32 index frame kNN = {32, 40, 51} from O 40 index frame kNN = {32, 40, 51} from O 51 index frame Access Latency = 7 frames. Tuning Time = 6 frames.

K-NN Queries(3) 10  Aggressive Approach  Access index table closer to the query point in order to shrink the search space more rapidly  Have small energy expense but high access latency ex. k = 3, a given query point p = 33. {6, 11, 17,?, 32, ?, ?, ?} from O 6 index frame Skip O 11, O 17, O 27. {6, 11, 17,?, 32, 40, 51, ?} from O 32 index frame {6, 11, 17,?, 32, 40, 51, 61} from O 40 index frame {6, 11, 17,?, 32, 40, 51, 61} from O 51 index frame Skip O 61, O 6, O 11, O 27. {6, 11, 17,27, 32, 40, 51, 61} from O 27 index frame Access Latency = 12 frames. Tuning Time = 5 frames.

Broadcast Reorganization(1) 11  The conservative and aggressive approaches represent a tradeoff between access latency and energy efficiency  Steps of reorganization  Divide into m broadcast segments with the same number of frames  Reconstruct by interleaving frames from these m segments. O6O6 O 11 O 17 O 27 O 32 O 40 O 51 O 61 m=2 O6O6 O 32 O 11 O 40 O 17 O 51 O 27 O 61

Broadcast Reorganization(2) 12  Example(Conservative) Access Latency = 6 frames Tuning Time = 4 frames ex. k = 3, a given query point p = 33. kNN = {6, 11, 32} from O 6 index frame kNN = {32, 40, 51} from O 32 index frame Ignore O 11 and Skip F 3 (O 11 ) kNN = {32, 40, 51} from O 40 index frame Ignore O 17 and Skip F5(O 17 ) kNN = {32, 40, 51} from O 51 index frame

Advantage & Disadvantage 13  Advantage of DSI  Fit the wireless broadcast environments  Allows query processing to start very quickly  Very resilient under error-prone  Disadvantage of DSI  How to determine an optimal exponential base(index base)