star-tree spatio-temporal self adjusting r-tree john tran duke university department of computer...
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STAR-Tree Spatio-Temporal Self Adjusting R-Tree
John TranDuke University
Department of Computer Science
Adviser: Pankaj K. Agarwal
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Problem Large Moving Data Sets
Many static data structures exist, but not many account for motion, which is realistic
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Examples of Use Geographic Information Systems
Air-Traffic Control
Protein Interactions
Traffic Patterns
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Defining the data
Can represent data as points in Rd
For our problem: Set of data points in R2: S = {p1, p2, …, pn} Can parameterize points to pi = (xi(t), yi(t))
Piecewise differentiable velocities
Bounding boxes can be represented by 2 points
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Queries
Query 1 – Report all points of S that lie inside rectangle R at time t
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Queries
Query 2 – Report all points of S that lie inside rectangle R at any time between t1 and t2
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Queries
Query 3 – Report the nearest neighbor of point in S
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R-Tree Bounding Box
Hierarchy All Children nodes
are bound by parents bounding box
Points are stored in leaf nodes
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STAR-Tree Same concept as
R-Tree Incorporate
movement into tree structure
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Conflicts
As bounding boxes change, overlap occurs Need to adjust for these overlap conflicts
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QT Implementation
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OpenGL Implementation
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Road Simplification Road data from US Bureau of
Census (TIGER) Paths are determined using
Dijkstra’s Shortest Path Algorithm Shapes of these paths are typically
simple but include many vertices Simplify path using Douglas-Peucker
heuristic (5 vertices max)
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Road Simplification Simplify road network
TIGER data is not perfect Polygonal chain with vertex lists Sometimes does not match roads that
should be matched
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Analysis of RDU RoadsV
ert
ices
wit
h n
str
eets
n streets
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Analysis of RDU Roads
n vertices
Str
eets
wit
h n
vert
ices
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Road Simplification
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Protein Shape Matching
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Problem Match two proteins based on
similarity or dissimilarity using intramolecular distance comparison
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Data Start from PDB files
Parse to get vertex list
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Calculating Distance Matrix Given a vertex list
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Calculating Distance Matrix Given a vertex list
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Defining cost
-GCTGATACTAGCT
| |||| |||||
GGGTGAT-GTAGCT
Let g(k) = +(k-1) is the cost of starting a new indel gap is the cost of continuing a gap
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Cost Function E(i,j) = min{D(i,j-1) + , E(i,j-1) + } F(i,j) = min{D(i-1,j) + , F(i-1,j) + } D(i,j) = min{D(i-1,j-1) + (i,j),
E(i,j), F(i,j)}
Where (i,j) = normalized sum of difference distance between Ai and all the matched vertices and Bj to the corresponding matched vertices
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Comparing identical Proteins
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Test Cases