On Monitoring the top-k Unsafe Places

1. On Monitoring the top-k Unsafe Places Donghui Zhang, Yang Du, Ling Hu Northeastern University ICDE’08, Cancun, Mexico

2. Problem (informal) • Police cars move around and protect neighborhoods. How to monitor the places that are under-protected? top-k unsafe place monitoring

3. Model • A centralized server stores the map of the city, along with the required protection of every place in the city. • A police car reports its position updates to the server. • The server maintains the top-k unsafe places. top-k unsafe place monitoring

4. rp: required protection • ap: actual protection • safety: ap - rp For each place: top-k unsafe place monitoring

5. Problem (formal) • Input: • a set of places: • rp • location (static) • a set of police cars: • protection region • location (keeps changing) • Output: • Continuously monitor the k places with the least safety. top-k unsafe place monitoring

6. Naïve Approach • Upon each location update (of a police car), compute the safety of every place. • Too slow… top-k unsafe place monitoring

7. BasicCTUP top-k unsafe place monitoring

8. Drawbacks of BasicCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • Flashing phenomenon. top-k unsafe place monitoring

9. Drawbacks of BasicCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • Flashing phenomenon. P  P: decrease the lower bound; Move again  decrease again (unnecessarily!) top-k unsafe place monitoring

10. Drawbacks of BasicCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • Many places in an illuminated cell maybe very safe! • Maintaining them increases cost. • Flashing phenomenon. top-k unsafe place monitoring

11. Drawbacks of BasicCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • Flashing phenomenon. • Assume a cell’s lower bound = SK. • Any police car move  decrease lower bound  illuminate (suppose no top-k place)  darken top-k unsafe place monitoring

12. OptCTUP • Unnecessary lower bound decreasing. In OptCTUP, decrease only once! (use a hash to avoid future decreasing) • Too many maintained places. • Flashing phenomenon. top-k unsafe place monitoring

13. OptCTUP • Unnecessary lower bound decreasing. In OptCTUP, in case P  F, may even increase the cell lower bound! • Too many maintained places. • Flashing phenomenon. top-k unsafe place monitoring

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16. OptCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • In OptCTUP, keep all cells dark. • Top-k unsafe places (and some more) are maintained. • The lower bound of a cell is computed as if the maintained objects do not exist. • Flashing cells increase cost. top-k unsafe place monitoring

17. OptCTUP • Unnecessary lower bound decreasing. • Too many maintained places. • Flashing phenomenon. • In OptCTUP, after a cell is illuminated, make sure its lower bound ≥ ∆ + SK. • Done by keeping some more objects in buffer. • This allows ∆ decreases before another illumination is necessary. top-k unsafe place monitoring

18. Experimental Setup • Network-based Generator of Moving Objects, Thomas Brinkhoff. top-k unsafe place monitoring

19. Initialization top-k unsafe place monitoring

20. Update cost top-k unsafe place monitoring

21. Conclusions • Proposed the CTUP query, which is a new addition to the family of continuous location-based queries. • Proposed Algorithm OptCTUP. • May be interesting to law enforcement agencies. Q & A... top-k unsafe place monitoring