1. Constructing a Message-Pruning Tree with Minimum Cost for Tracking Moving Objects in Wireless Sensor Networks Is NP- Complete and an Enhanced Data Aggregation Structure IEEE TRANSACTIONS ON COMPUTERS, VOL. 57, NO. 6, JUNE 2008 Presented By Yen-Yi, Hsu

2. Contents 1.Introduction 2.Related Work 3.Preliminaries 4.Reference 1 5.Reference 2 6.Hardness of Min-Cost Message-Pruning Tree 7.New Data Aggregation Structure 8.Performance Study 9.Conclusion 2

3. Introduction  WSNs be used in a wide range of applications ex: environment monitoring, battlefield surveillance, health care  One of the most important areas of research ─ object tracking  Two basic operation ： Update and Query  The Object’s location stored in the sink or not  Construct the message-pruning tree with shortcuts 3

4. Related Works  How to monitor the object  This paper: address now to aggregate the sensed data  Dual prediction using the moving history  Tree topology  Distributed database and a message-pruning tree: attempt to prune redundant message 4

5. Preliminaries  Voronoi graph  Assume that the sensor that receives the strongest signal from an object is responsible for reporting the object’s location 5

6. Preliminaries  Undirected Weighted Graph  Assumed that the event rate between any two neighboring sensors can be statistically calculated  Assumed that the sensor’s transmission range is large enough such that any two neighbors can directly communicate with each other  Represented as G(V G,E G,w G ) 6

7. Preliminaries  Undirected Weighted Graph  Assumed that the event rate between any two neighboring sensors can be statistically calculated  Assumed that the sensor’s transmission range is large enough such that any two neighbors can directly communicate with each other  Represented as G(V G,E G,w G ) 7

8. Preliminaries  Message-Pruning Tree  T(V T,E T,w T ), rooted at the sink  w T (u,v): minimum hop count between u and v in G.  V T =V G and E T E G 8

9. Preliminaries  Database Update  Each node v maintains a list v.DL=(L 0, L 1, L 2, …, L k ), where k is the number of v’s children  For example, L 0 =L 2 =NIL and L 1 ={Car1} in b.DL 9

10. Preliminaries  Database Update  When a object o moves from u to neighbor v dep(o, u, v) arv(o, u, v) Along to the tree path to lca(u, v)  dist T (g, h) = w T (g, d)+w T (d, b) +w T (b, e)+w T (e, i) +w T (i, h)=5  The cost of updating the database is 10

11.  Object Query  Forwarding path for Car1 (a, b, d, g)  (a, b, d)  When a sensor receives a query for object o, it forwards the query to its ith child if o L i and it’s ith child is not a leaf  The cost of a query for object is double the sum of w T s of edges on the reduced forwarding path Preliminaries 11

12. Preliminaries  Object Query  For example: the cost of a query for Car1 is 2 x dist T (a, d) = 4  The cost of querying objects is where q(v) denotes the query rate of sensor v 12

13. Reference  Efficient In-Network Moving Object Tracking in Wireless Sensor Networks  Chih-Yu Lin, Student Member, IEEE, Wen-Chih Peng, Member, IEEE, and Yu-Chee Tseng, Senior Member, IEEE  IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 5, NO. 8, AUGUST 2006 13

14. Update Cost  counting the average number of messages transmitted in network per unit time  (2) 14 vp(v)

15. Deviation-Avoidance Tree  1. We would expect that dist T (u, sink)= dist G (u, sink)  otherwise, u deviates from its shortest path to the sink 15

16. Deviation-Avoidance Tree  2. minimize the w T (u, v)  by selecting neighboring sensors as parents  avg. of dist T (u, lca(u, v))+dist T (v, lca(u, v)) can be minimized 16

17. Deviation-Avoidance Tree  3. an edge with higher w G (u, v) should be included into T as early as possible  highest-weight-first principle   For two edges (u, v) and (u’, v’) E G such that w G (u, v) > w G (u’, v’), it’s desirable that 17

18. Deviation-Avoidance Tree  T is always a subgraph of G  w T (u, v)=1 18

19. Zone-Based DAT 19

20. Zone-Based DAT 20

21. Query Cost Reduction  QCR tries to adjust the tree T obtained by DAT or Z-DAT in a bottom-up manner  Two observation 1.Placing a node as a leaf can save the query cost 2.We should choose a node closer to the sink as v’s parent, 21

22. Query Cost Reduction  1. if a node v is not a leaf 22

23. Query Cost Reduction  2. if a node v is a leaf node 23

24. Reference  Message-Ef fi cient In-Network Location Management in a Multi-sink Wireless Sensor Network  Chih-Yu Lin and Yu-Chee Tseng, Ten H. Lai 24

25. Multi-sink WSNs  Naïve way to extend a single-sink system to multi- sink system is to construct a virtual tree for each sink x  Three issues need to be addressed when multiple trees coexist  1. Update and query mechanisms  2. Multi-tree construction  3. The number of trees used 25

26. Update and Query Mechanisms  We denote a WSN with n sensors, m of which are designated as sinks ( σ i, i =1,..., m)  rooted at σ i has constructed form G  Each sensor x keeps two tables  Subtree_Member S X : An m x n table to indicate whether another sensor is a descendant of x in a certain tree  Detected_List DL X : k+1 entries, each entry maintain a set of objects 26

27.  For Example  Subtree_Member S D (T B,F)=1 S D (T A,F)=0  Detected_List Car2 DL A (D) D is a neighbor of A S D (T A,G)=1 and Car1 is tracked by G I D F J A B C E G H K Car1 Car3 Car2 Update and Query Mechanisms 27

28.  1. The Location Update Mechanism  Update message should be sent from a and b to lca i (a, b)  In a system with m trees, a sensor x need to maintain p i (x) for each  Because the number of neighbors of x may be smaller than m, some of the p i (x) may be duplicate and thus can be update together  Thus, update mechanism comprise two parts: (1.) Forwarding Rule (2.) Updating Rule Update and Query Mechanisms 28

29.  (1.)Forwarding Rule  If there is a tree making Eq.1 true, the update message should be sent to p i (x)  If two trees both satisfy Eq.1 and p i (x) = p j (x), then only one update message needs to be sent  (2.)Updating Rule Update and Query Mechanisms 29

30. Update and Query Mechanisms 30

31.       Update and Query Mechanisms 31

32.  2. The Location Query Mechanism  Assume user can issue a query from any sensor (1) o does not appear in any of the entries of DL X –x will forward the query to the closest sink –If an intermediate node y finds that o appears in DL y, then the second scenario will be initiated immediately (2) o appears at least in one of the entries of DL X –Model the WSN responsible for tracking object o as a directed query graph Update and Query Mechanisms 32

33. Update and Query Mechanisms 33

34. Update and Query Mechanisms 34

35. Multi-Tree Construction  1. The MT-HW Algorithm (with the high-weight-first property)  an edge (u, v) with higher weight will be considered for being included into a tree earlier  candidate parents : distG( σ i, x) = distG( σ i, y) +1 and y is x’s neighbor  Each sensor x will sort its neighbors in a decreasing order according to the event rates  Then, for each sink σ i, x will pick one neighbor y as its parent that has the highest event rate among x’s candidate parents for σ i and set y= pi(x) 35

36. Multi-Tree Construction  2. The MT-EO Algorithm (with the edge-overlap-first property)  If we can increase the number of the tree edges that overlap with each other, SC(v) ↑ and U ↓  Each of x’s neighbors is associated with an overlap counter for x  Then, x select the neighbor y whose overlap counter is the largest  Until x has determined its paents for all sinks 36

37. Simulation Results  Comparison of Update Costs 37

38. Simulation Results  Comparison of total costs under different query rate 38

39. Simulation Results  Comparison of total cost (single vs. multiple) 39

40. Simulation Results  Two implicit results should be addressed  1. multi-sink system has a faster query response time 40

41. Simulation Results  2. multi-sink system can achieve a better load balance factor 41

42. Hardness of MC-MPT  Exact 3-cover problem  Given a S= { σ 1,…, σ s } of triplets of elements from a set L={ τ 1,…, τ 3t }, is there a subcollection S’ S of size t that covers L?  Ex: L={ }, S={ } is given, S’={ } is a solution of this problem  Minimum-Cost Message-Pruning Tree  G(V G, E G, w G, q G ), a sink sink, integer M≥0  Determine whether there exist a T(V T, E T ) rooted at sink with V T =V G whose cost U(T)+Q(T) is at most M 42

43. Hardness of MC-MPT 43

44. Hardness of MC-MPT 44

45. New Data Aggregation Structure  When Car1 moves: g → h  Reduced forwarding path: (a, b, e,i)  The cost of a query is 6  This paper’s idea:  Add a shortcut (d → h) 45

46. New Data Aggregation Structure  After add a shortcut:  Reduced forwarding path: (a, b, d)  The cost of updating the database: w T (g, d)+w T (d → h)=2  The cost of a query for Car1: 2x( w T (a, b)+w T (b, d))=4 46

47. New Data Aggregation Structure  The Structure  The shortcut (u → v) will be u’s outgoing shortcut and v’s incoming shortcut  w T (u → v) = dist G (u, v)  For example, w T (d → h) = 1  (u 1, u 2, …, u n ) is a downward path if u i is the parent of u i+1 (u i →u i+1 ) is a shortcut  (b, d, h) is a shortest downward path from b to h 47

48.  The Structure  v.DL( ) k is the number of v’s children p is the number of v’s outgoing shortcut q is the number of v’s incoming shortcut  d.DL(NIL, NIL, {Car1}) New Data Aggregation Structure 48

49.  The Structure  Extended_ancestor: ex: a, b, d, e, i and h are extended_ancestor of h  u.prec(o) ex: h.prec(Car1) = d  can be evaluated by checking DL  u.succ(v) ex: d.succ(h) = h and b.succ(h) = d New Data Aggregation Structure 49

50.  Object Query New Data Aggregation Structure 50

51.  Example  sink a receive query(Car1))  The cost of a query(o) is 2 x dist(r fpath(query(o)))  The cost of queries for all objects is 2 x New Data Aggregation Structure 51

52.  Database Update New Data Aggregation Structure 52

53.  Example New Data Aggregation Structure  The cost of updating the database for all events 53

54.  Addition of Shortcuts  Add shortcut (u → v) with the property 1. dist T (sink,u)+w T (u→v) ≦ dist T (sink,v) 2. (u, v) E G -E T 3. u is not a leaf New Data Aggregation Structure 54

55. Performance Study  256 sensors, 32 x 32 sensing field  Random & regular deployment  Z-DAT and Z-DAT+QCR were constructed  α and δ are set to 4 and 0  the tree root in Z-DAT or Z-DAT+QCR is located in either the corner or the center  averaging the data of 1000 simulations 55

56. Performance Study  The Cost of Updating the Database 56

57. Performance Study  The Cost of Updating the Database 57

58. Performance Study  The Cost of Updating the Database 58

59. Performance Study  The Cost of Updating the Database 59

60. Performance Study  The Cost of Querying Objects 60

61. Performance Study  The Cost of Querying Objects dist T (sink,u)+w T (u→v)=dist T (sink,v) 61

62. Conclusion  Total cost = Update cost + Query Cost  Multiple sink is important when the network scale is large or when the query rate is high  It proposed a data aggregation structure that is constructed by adding shortcuts to MPT 62