Graphics Application Lab

Myoung-Ah Kang, Sylvie Servigne,Ki-Joune Li, Robert Lau-rini

CIKM’ 99

Kim Hyong-Jun, Yoon Tai-JinGA Lab.

Indexing Field Values in Field Oriented Systems : Interval Quadtree

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Motivation

Query based on given position

Query based on given field value

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Notation for field Representa-tion

Field Representation

Digital Elevation Model (DEM)

Triangulated Irregular Network (TIN)

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Notation for Field Queries

Field Query Variableso Spatial variable : So Value variable : V

Query Representation

Q1 : f 1 (S) = V (Find field value on a given area S.)Q2 : f 1 (V) = S (Find region with a given field value V.)

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Subfield & Field Query Pro-cessing

Subfield

F i = (Ai , Vmin,i , Vmax,i )

Fieldvalue

Space(x,y)

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Subfield & Field Query Pro-cessing

Quadtree

54,62

49,59 46,56

55,65

64,7468,78

59,68

64,70

73,80

60,66 65,75

58,69 64,73

1(46,80)

2(58,75)

3(73,80) 4(64,70)

5(46,78)

6(60,66)7(65,75) 8(58,69)9(64,73) 10(68,78)11(64,74)12(59,68)

13(54,62)14(55,65)15(49,59) 16(46,56)

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Field Query Processing Strat-egy

Step 1 (filtering step) : find all subfields whose interval overlaps with [50,60]

54,62

49,5946,56

55,65

64,7468,78

59,68

64,70

73,80

60,66 65,75

58,69 64,73

Step 2 (refinement step) : retrieve all field objects in the selected subfields by step 1

Step 3 (estimation step) : estimate the region where value is between [50,60] based on the low level representation method of field

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Pointer-based Quadtree

1(46,80)

2(58,75)

3(73,80) 4(64,70)

5(46,78)

6(60,66)7(65,75) 8(58,69)9(64,73) 10(68,78)11(64,74)12(59,68)

13(54,62)14(55,65)15(49,59) 16(46,56)

Procedure Field value indexingBy Pointer Quadtree

Input: P(root node of quadtree) I (given field values) Output: B (set of field objects)

A = {P}. B = {}. while A is not empty, m = delete a node in A. if A is non-leaf & interval(m) overlaps with I, then insert four child nodes into A. if m is leaf node & interval(m) overlaps with I, then insert the field objects of m into B End whileEnd procedure

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Pointer Quadtree Weak points

Relatively a large amount of storage space and it leads to frequent disk accesses when following pointers

scattered on several branches of quadtree, we must traverse many paths in the quadtreeo Re organized using a tree structure in form of B-

tree or one of its variations

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Interval Quadtree

Transformation invervals of field values

Leaf node = (Sid , Nid , Size ,Vmin , Vmax , D) Subfield 6

50 60

Subfield 5

Subfield 3

Subfield 4

Subfield 2Subfield 1

Field value

Original Field value Dimen-sion

max

min

3

6

24

1

5

50

60

Transformed Space

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Implementaion and Perfor-mance

RelativeInterval sizeof thresh-old

Number ofsub-fields

Height ofR*-tree

Filter-ingtime(ms)

Refine-ment time(ms)

0.05 52204 4 145 96

0.1 15724 3 36 69

0.2 3889 3 7 76

0.3 2077 3 3 109

0.4 1423 3 2 113

0.5 898 2 1 139

0.6 406 2 1 149

0.7 37 2 0.1 162

0.8 19 1 0.01 72

0.9 13 1 0.01 72

0.95 4 1 0.01 170

Comparison betwwen Interval Quadtree with R*-tree and Lin-ear scanning

Some variables according to the relative interval size of thresh-old

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Comparison of proposed method

Camparison of proposed indexing structuresConstructed R*-tree with 3-d rectangles of subfields obtained

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Conclusion

Divide a field into several subfiledso Difference between the max value and min

valueo Use Quadtree for division

Proposed and evaluated two indexing structures o Pointer-based Quadtreeo Interval Quadtreeo R*-tree for benchmark