1. 1 Spatial-temporal Database and moving objects management

2. 2 Outlines Introduction Background knowledge Spatial database Spatial-temporal database Moving objects management Conclusions

3. 3 Introduction

4. 4 Location-aware database services  GPS technology  GIS system  Vehicular database  Wireless communication technology Location update Query Answer

5. 5 Introduction Location-based applications  Traffic monitoring and management  Location-based store (services) find and advertisement  People cooperation and communication

6. 6 Various Queries How many cars in this area? Static Query over moving Object Location-aware Database Server Keep talking with 3 nearest police cars Moving Query over moving Object Continuous K-nearest Neigbor How many cars in Highlight now? Moving Query over moving Object Snapshot Moving Query over Static Object Keep me updated by hospitals in 3 miles Keep updating how many airplanes within 100 miles Moving Query over moving Object Continuous Range Based

7. 7 Target Query Moving Continual Queries over moving object (MCQ)  Generalization of Moving and Static Queries  Continuous nature 1 continuous query = a sequence of snapshot queries with some frequency  Range-based or kNN

8. 8 Background knowledge

9. 9 History of Database Technology 1960s : Data collection, database creation, IMS and network DBMS 1970s : Relational data model, relational DBMS implementation 1980s : RDBMS, advanced data models (extended- relational, OO, deductive, etc.) and application-oriented DBMS (spatial, scientific, engineering, etc.) 1990s — 2000s : Data mining and data warehousing, multimedia databases, and Web databases

10. 10 Structure of a RDBMS A DBMS is an OS for data! A typical RDBMS has a layered architecture. Query Optimization and Execution Relational Operators Files and Access Methods Buffer Management Disk Space Management DB Modern Database Systems Extend these layers

11. 11 Index Methods for RDBMS Hashing Methods B-tree family Both of them are one-dimensional

12. 12 B+-tree Records must be ordered over an attribute Queries  exact match or range queries over the indexed attribute find the name of the student with SID=dr868301 find all students with gpa between 3.00 and 3.5

13. 13 B+-tree:properties “ B ” for balance! Each node contains up to n-1 search key values and n pointers A nonleaf node may hold up to n pointers and must hold at least Two types of nodes: index nodes and data nodes; each node is 1 page (disk based method)

14. 14 57 81 95 to keys to keysto keys to keys < 57 57  k<8181  k<95 95  Index node

15. 15 Data node 57 81 95 To record with key 57 To record with key 81 To record with key 85 From non-leaf node to next leaf in sequence

16. 16 EX: B+ Tree of order 3. (a) Initial tree 60 80 20, 40 205,106040,5080,100 Index level Data level

17. 17 Query Example Root 100 120 150 180 30 3 5 11 30 35 100 101 110 120 130 150 156 179 180 200 Range[32, 160]

18. 18 Insertion Find correct leaf L. Put data entry onto L.  If L has enough space, done!  Else, must split L (into L and a new node L2) Redistribute entries evenly, copy up middle key. Insert index entry pointing to L2 into parent of L. This can happen recursively  To split index node, redistribute entries evenly, but push up middle key. (Contrast with leaf splits.) Splits “ grow ” tree; root split increases height.  Tree growth: gets wider or one level taller at top.

19. 19 Deletion Start at root, find leaf L where entry belongs. Remove the entry.  If L is at least half-full, done!  If L has only d-1 entries, Try to re-distribute, borrowing from sibling (adjacent node with same parent as L). If re-distribution fails, merge L and sibling. If merge occurred, must delete entry (pointing to L or sibling) from parent of L. Merge could propagate to root, decreasing height.

20. 20 Create a B+ tree Insertion order: 9, 6, 1, 8, 4, 13 6, 9 1 6 1 6, 8 68, 9 1, 4 6, 8 68, 9 8 61, 49,138 6 9

21. 21 Insert a key Insert a key into a leaf which still has some room (not overflow). Put the keys of this leaf in order. No changes are made in the index level. 1 6 6, 91, 4 6 6, 9 insert 4

22. 22 If a key is inserted into a full leaf (overflow)  Split, the new leaf node is included in the sequence set, keys are distributed evenly between the old and the new leaves, and the first key from the new node is copied (not moved, as in B-tree) 1, 4 6 6, 91, 4 6, 9 6 The parent is not fullThe parent is full Insert 10 9,10 Insert 3 1 3 69,103, 4 6 6, 9

23. 23 Delete a key Delete a key from a leaf leading to no underflow Delete the leaf and keep remaining keys in order  index level ! delete 4 1, 4 6, 9 6 9,10 1 6, 9 6 9,10 delete 9 1, 4 6, 10 6 10 1, 4 6, 9 6 10

24. 24 Spatial database

25. 25 Introduction A common technology for some Applications:  GIS (geographic/geo-referenced data)  VLSI design (geometric data)  modeling complex phenomena (spatial data) All need to manage large collections of relatively simple spatial objects

26. 26 SDBMS Definition A spatial database system: Is a database system  A DBMS with additional capabilities for handling spatial data Offers spatial data types (SDTs) in its data model and query language  Structure in space: e.g., POINT, LINE, REGION  Relationships among them: (l intersects r) Supports SDT in its implementation providing at least  spatial indexing (retrieving objects in particular area without scanning the whole space)  efficient algorithms for spatial joins (not simply filtering the cartesian product)

27. 27 Modeling Assume 2-D and GIS application, two basic things need to be represented: Objects in space: cities, forests, or rivers single objects Coverage/Field: say something about every point in space (e.g., partitions, thematic maps) spatially related collections of objects

28. 28 Modeling: spatial primitives for objects Point: object represented only by its location in space, e.g. center of a state Line (actually a curve or ployline): representation of moving through or connections in space, e.g. road, river Region: representation of an extent in 2d- space, e.g. lake, city

29. 29 Modeling: spatial relationships Topological relationships: e.g. adjacent, inside, disjoint.  Are invariant under topological transformations like translation, scaling, rotation Direction relationships: e.g. above, below, or north_of, sothwest_of, … Metric relationships: e.g. distance

30. 30 Spatial Queries Given a collection of geometric objects (points, lines, polygons,...) organize them on disk, to answer efficiently  point queries  range queries  k-nn queries

31. 31 Spatial Queries Given a collection of geometric objects (points, lines, polygons,...) organize them on disk, to answer  point queries  range queries  k-nn queries

32. 32 Spatial Queries Given a collection of geometric objects (points, lines, polygons,...) organize them on disk, to answer  point queries  range queries  k-nn queries

33. 33 Spatial Queries Given a collection of geometric objects (points, lines, polygons,...) organize them on disk, to answer  point queries  range queries  k-nn queries

34. 34 Access Methods Discussed in the course  Grid file  K-d tree  Z curve  R-tree

35. 35 The problem Given a point set and a rectangular query, find the points enclosed in the query (range) Given a point set and a point query q, find the point nearest to q (NN,KNN) Query

36. 36 Grid File Idea: Use a grid to partition the space  each cell is associated with one page Two disk access principle

37. 37 Grid File Start with one bucket for the whole space. Select dividers along each dimension. Partition space into cells Dividers cut all the way.

38. 38 Grid File Each cell corresponds to 1 disk page. Many cells can point to the same page. Cell directory potentially exponential in the number of dimensions

39. 39 Grid File Implementation Dynamic structure using a grid directory  Grid array: a 2 dimensional array with pointers to buckets (this array can be large, disk resident) G(0, …, nx-1, 0, …, ny-1)  Linear scales: Two 1 dimensional arrays that used to access the grid array (main memory) X(0, …, nx-1), Y(0, …, ny-1)

40. 40 Example Linear scale X Linear scale Y Grid Directory Buckets/Disk Blocks

41. 41 Grid File Search Exact Match Search: at most 2 I/Os assuming linear scales fit in memory.  First use liner scales to determine the index into the cell directory  access the cell directory to retrieve the bucket address (may cause 1 I/O if cell directory does not fit in memory)  access the appropriate bucket (1 I/O) Range Queries:  use linear scales to determine the index into the cell directory.  Access the cell directory to retrieve the bucket addresses of buckets to visit.  Access the buckets.

42. 42 K-d tree K-d tree is a main memory binary tree for indexing k-dimensional points The kd-tree is a data structure that is based on recursively subdividing a set of points with alternating axis-aligned hyperplanes. K-d tree is not necessarily balanced

43. 43 Kd-trees l1l1 l8l8 1 l2l2 l3l3 l4l4 l5l5 l7l7 l6l6 l9l9 l 10 3 245 11 9 10 6 87 4 7 6 5 1 3 2 9 8 11 l5l5 l1l1 l9l9 l6l6 l3l3 l 10 l7l7 l4l4 l8l8 l2l2

44. 44 Kd-trees. Construction 4 7 6 5 1 3 2 9 8 10 11 l5l5 l1l1 l9l9 l6l6 l3l3 l 10 l7l7 l4l4 l8l8 l2l2 l1l1 l8l8 1 l2l2 l3l3 l4l4 l5l5 l7l7 l6l6 l9l9 3 245 11 9 10 6 87

45. 45 Z-ordering Map points from 2-dimensions to 1-dimension. Use a B+-tree to index the 1-dimensional points Basic assumption: Finite precision in the representation of each co-ordinate, K bits (2 K values) The address space is a square (image) and represented as a 2 K x 2 K array

46. 46 Z-ordering Impose a linear ordering on the pixels of the image  1 dimensional problem 00011011 00 01 10 11 A B Z A = shuffle(x A, y A ) = shuffle(“01”, “11”) = 0111 = (7) 10 Z B = shuffle(“01”, “01”) = 0011

47. 47 Z-ordering Given a point (x, y) and the precision K find the pixel for the point and then compute the z-value Given a set of points, use a B+-tree to index the z-values A range (rectangular) query in 2-d is mapped to a set of ranges in 1-d

48. 48 Queries Find the z-values that contained in the query and then the ranges 00011011 00 01 10 11 Q A  range [4, 7] QAQA QBQB Q B  ranges [2,3] and [8,9]

49. 49 R-trees [Guttman 84] Main idea: allow parents to overlap!  => guaranteed 50% utilization  => easier insertion/split algorithms.  (only deal with Minimum Bounding Rectangles - MBRs)

50. 50 R-trees A multi-way external memory tree Index nodes and data (leaf) nodes All leaf nodes appear on the same level Every node contains between m and M entries The root node has at least 2 entries (children)

51. 51 R-Tree

52. 52 R-Tree 2 0 46 8 10 2 4 6 8 x axis y axis b c a d e f g h i j k l m Range query: find the objects in a given range. E.g. find all hotels in Boston. No index: scan through all objects. Inefficient! B+-tree: only cluster based on one dim. Inefficient!

53. 53 R-Tree: Clustering by Proximity

54. 54 R-Tree

55. 55 R-Tree

56. 56 R-Tree 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7

57. 57 R-tree properties a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 disk-based: stored on disk, load to memory the needed part. balanced: all leaf nodes have the same distance from root. dynamically-updateable: dynamic insertion/deletion leaf-storage: all records are stored in leaf nodes. min-capacity: every node (except the root) is at least half full.

58. R-Tree structure leaf entry = index entry =  MBR of all objects in the subtree. Observation: if Q does not intersect an MBR, no object in the sub-tree is inside Q. Q MBR

59. 59 MBR face property MBR is a d-dimensional rectangle, which is the minimal rectangle that fully encloses (bounds) an object (or a set of objects) MBR f.p.: Every face of the MBR contains at least one point of some object in the database

60. Range query (given range Q) Start at root. 1. If current node is non-leaf, for each entry, if box E overlaps Q, search subtree identified by ptr. 2. If current node is leaf, for every object in the leaf page, report if contained in Q.

61. 61 Range Query 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7

62. 62 Range Query 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7

63. 63 KNN Search in a R tree Visit an MBR (node) only when necessary How to do pruning? Using MINDIST and MINMAXDIST

64. 64 MINDIST MINDIST(P, R) is the minimum distance between a point P and a rectangle R If the point is inside R, then MINDIST=0 If P is outside of R, MINDIST is the distance of P to the closest point of R (one point of the perimeter)

65. 65 MINDIST computation MINDIST(p,R) is the minimum distance between p and R with corner points l and u  the closest point in R is at least this distance away r i = l i if p i < l i = u i if p i > u i = p i otherwise p p p R l u MINDIST = 0 l=(l 1, l 2, …, l d ) u=(u 1, u 2, …, u d )

66. 66 MINDIST and MINMAXDIST MINDIST(P, R) <= NN(P) <=MINMAXDIST(P,R) R1 R2 R3 R4 MINDIST MINMAXDIST MINDIST MINMAXDIST MINDIST

67. Insert object o Start at root and go down to “ best-fit ” leaf L.  Go to child whose box needs least enlargement to cover B; resolve ties by going to smallest area child. If best-fit leaf L has space, insert entry and stop. Otherwise, split L into L1 and L2.  Adjust entry for L in its parent so that the box now covers (only) L1.  Add an entry (in the parent node of L) for L2. (This could cause the parent node to recursively split.)

68. 68 E.g. 1: no split, no enlargement 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 insert o o

69. 69 E.g. 2: no split, but enlargement 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 insert o o

70. 70 E.g. 2: no split, but enlargement 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 insert o o

71. 71 E.g. 3: split 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i j k E 6 E 6 E 7 insert o o

72. 72 E.g. 3: split 2 0 46 8 10 2 4 6 8 x axis y axis b c a E 1 d e f g h i j k l m E 2 a b cd e E 1 E 2 E 3 E 4 E 5 Root E 1 E 2 E 3 E 4 f g h E 5 l m E 7 i o j E 6 E 6 E 7 k o E’ 6

73. 73 R-trees: Variations R+-tree: DO not allow overlapping, so split the objects (similar to z-values) R*-tree: change the insertion, deletion algorithms (minimize not only area but also perimeter, forced re-insertion )

74. 74 Spatio-Temporal Databases

75. 75 Introduction Spatio-temporal Databases: manage spatial data whose geometry changes over time Geometry: position and/or extent Global change data: climate or land cover changes Transportation: cars, airplanes Animated movies/video DBs

76. 76 ST DBs A special Temporal Database  All the features of temporal database  Attributes can be spatial also Extension of Spatial Databases  Objects change instead of being static  At any timestamp it is a conventional Spatial Database New Database type

77. 77 Requirements Efficient Representation of Space and Time Data Models Query Languages Query processing and Indexing GUI for spatio-temporal datasets

78. 78 Spatio-temporal Objects

79. 79 ST Queries Range Queries: “find all objects contained in a given area Q at a given time t” NN queries: “find which object became the closest to a given point s during time interval T,” Aggregate queries: “find how many objects passed through area Q during time interval T,” or, “find the fastest object that will pass through area Q in the next 5 minutes from now”

80. 80 ST Queries join queries: “given two spatiotemporal relations R1 and R2, find pairs of objects whose extents intersected during the time interval T,” or “find pairs of planes that will come closer than 1 mile in the next 5 minutes” similarity queries: “find objects that moved similarly to the movement of a given object o over an interval T”

81. 81 SP Data Types Moving Points  Extent does not matter  Each object is modeled as a point (moving vehicles in a GIS based transportation system) Moving regions  Extent matters!  Each object is represented by an MBR, the MBR can change as the object move (airplanes, storm, … )

82. 82 SP Data Types Different Type of changes:  Changes are applied discretely Urban planning: appearance or dis-appearance of buildings  Changes are applied continuously Moving objects (eg. Vehicles)

83. 83 Trajectories Moving objects create trajectories Usually we can sample the positions of the objects at periodic time intervals  t Linear Interpolation:easy and usually accurate enough Trajectory: a sequence of 2 or 3-dim locations

84. 84 Temporal Environment Valid time Two types of environments:  Predicting the future positions: Each object has a velocity vector. The DB can predict the location at any time t>t now assuming linear movement. Queries refer to the future  Storing the history. Queries refer to the past states of the spatial database

85. 85 The Historical Environment Spatio-temporal Evolution

86. 86 Indexing using R-trees Assume that time is another dimension, use a 3D R-tree Store the objects as their 3D MBR. How to compute that?

87. 87 Problems of 3D R-tree How to store “ now ” ? Use a large value … Long lived objects will have very long MBRs, difficult to cluster Extensive overlap and empty space  bad query performance for specific queries Also, works only for discrete changes

88. 88 Indexing Moving Objects The problem of indexing any type of moving objects can be reduced to indexing discrete rectangles. Continuous pointsContinuous rectanglesDiscrete rectangles x y time t

89. 89 Historical R-trees (HR-trees) o1o1 o2o2 o6o6 o7o7 o5o5 p1p1 p2p2 p3p3 o1o1 o2o2 o3o3 o4o4 o5o5 o6o6 o7o7 p1p1 p2p2 p3p3 o4o4 o3o3 timestamp 1 An R-tree is maintained for each timestamp in history. Trees at consecutive timestamps may share branches to save space.

90. 90 Historical R-trees An R-tree is maintained for each timestamp in history. Trees at consecutive timestamps may share branches to save space. p1p1 p2p2 p3p3 o1o1 o2o2 o3o3 o4o4 o5o5 o6o6 o7o7 timestamp 1p1p1 p2’p2’p3’p3’ o3o3 o4o4 timestamp 2 o3o3 o4o4 o5’o5’ o1o1 o2o2 o6o6 o7o7 o5’o5’ p1p1 p2’p2’ p3’p3’ o4o4 o3o3

91. 91 HR-trees: Pros and Cons HR-trees answer timestamp queries very efficiently. –A timestamp query degenerates into a spatial window query handled by the corresponding R-tree at the query timestamp. Not quite efficient: –Expensive space consumption. A node needs to be duplicated even when only one object moves. –Interval query processing is inefficient. Although redundancy (from duplication) is necessary to maintain good timestamp query performance, it is excessive in HR-trees.