1. Graphics Application Lab Myoung-Ah Kang, Sylvie Servigne,Ki-Joune Li, Robert Laurini CIKM’ 99 Kim Hyong-Jun, Yoon Tai-Jin GA Lab. Indexing Field Values in Field Oriented Systems : Interval Quadtree

2. Graphics Application Lab Motivation 2 Query based on given position Query based on given field value

3. Graphics Application Lab Notation for field Representation  Field Representation 3 Digital Elevation Model (DEM) Triangulated Irregular Network (TIN)

4. Graphics Application Lab Notation for Field Queries  Field Query Variables oSpatial variable : S oValue variable : V  Query Representation 4 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.)

5. Graphics Application Lab Subfield & Field Query Processing  Subfield 5 F i = (A i, V min,i, V max,i ) Field value Space(x,y)

6. Graphics Application Lab Subfield & Field Query Processing  Quadtree 6 54,62 49,5946,56 55,65 64,74 68,78 59,68 64,70 73,80 60,66 65,75 58,6964,73 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)

7. Graphics Application Lab Field Query Processing Strategy Step 1 (filtering step) : find all subfields whose interval overlaps with [50,60] 7 54,62 49,5946,56 55,65 64,74 68,78 59,68 64,70 73,80 60,66 65,75 58,6964,73 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

8. Graphics Application Lab Pointer-based Quadtree 8 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 indexing By 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 while End procedure

9. Graphics Application Lab 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 quadtree oRe organized using a tree structure in form of B-tree or one of its variations 9

10. Graphics Application Lab Interval Quadtree  Transformation invervals of field values 10 Leaf node = (S id, N id, Size,V min, V max, D) Subfield 6 5060 Subfield 5 Subfield 3 Subfield 4 Subfield 2 Subfield 1 Field value Original Field value Dimension max min 3 6 2 4 1 5 50 60 Transformed Space

11. Graphics Application Lab Implementaion and Performance 11 Relative Interval size of threshold Number of subfields Height of R*-tree Filtering time(ms) Refinement time(ms) 0.0552204414596 0.11572433669 0.238893776 0.3207733109 0.4142332113 0.589821139 0.640621149 0.73720.1162 0.81910.0172 0.91310.0172 0.95410.01170 Comparison betwwen Interval Quadtree with R*-tree and Linear scanning Some variables according to the relative interval size of threshold

12. Graphics Application Lab Comparison of proposed method 12 Camparison of proposed indexing structures Constructed R*-tree with 3-d rectangles of subfields obtained

13. Graphics Application Lab Conclusion  Divide a field into several subfileds oDifference between the max value and min value oUse Quadtree for division  Proposed and evaluated two indexing structures oPointer-based Quadtree oInterval Quadtree oR*-tree for benchmark 13