Download Q 5.2 : Consider the rough guide to worst

Q 5.2 : Consider the rough guide to worst-case time complexity of algorithms (Table 5.2, pp. 171).
Classify the complexity of following algorithms into classes of constant, logarithmic, linear,
n*log(n), polynomial and exponential: Assume relevant line-strings have N segments, polygons
have N vertices and graphs have N vertices and E edges.
1. Douglas-Pucker algorithm to discretize arcs (sec. 5.2.3, pp. 176-177)
linear
2. Compute area of a simple polygon (sec. 5.5.1, pp. 195-197)
linear
3. Compute centroid of a polygon (sec. 5.5.1, pp. 195-197)
linear
4. Point in polygon (sec. 5.5.2, pp. 197-199)
linear
5. Intersection or a polygon-pair, each with N vertices (sec. 5.5.3, pp. 201-202)
polynomial (simple algorithm)
linear (winged-edged structures)
6. Depth-first or breadth-first graph traversal (sec. 5.7.2, pp. 213-217)
linear
7. Single-pair shortest path in a graph (sec. 5.7.2, pp. 213-217)
polynomial (simple algorithm)
n*log(n) (better data structure)
8. All-pair shortest paths in a graph (sec. 5.7.2, pp. 213-217)
polynomial
9. Hamiltonian circuit (or Traveling salesman problem) (sec. 5.7.2, pp. 213-217)
exponential
Q 5.4 : Consider alternative data models for spatial object domain (section 5.3, pp. 177-187)
including spagetti, node-arc-area, DCEL, etc. Which data model is closest to the following popular
formats:
1. GML Simple Features
spaghetti. No topological information
2. ESRI Shapefile: wikipedia article
spaghetti. No topological information
Q 6.2 : Compare and contrast R-trees and R+-trees. Consider a minimum orthogonal bounding
rectangle for rectangle T and L. Add it to the set of rectangles in Fig. 6.29 (pp. 253) and Fig. 6.30
(pp. 254). Redraw the R-tree and R+tree in Fig. 6.29 and 6.30 if this new rectangle is inserted.
Briefly justify your solutions by recalling how R-tree and R+tree deal with large objects based on
narrative of section 6.6.2 (pp. 252-254)?
They both use Minimum bounding boxes and they are both balanced tree.
The big difference between R tree and R+tree is that R tree allows overlap in the non-leaf nodes,
while R+tree doesn’t allow overlap in the non-leaf nodes. R+ tree has better search performance
for large object, but it also needs more complex insertion and deletion algorithm.
R-tree:
When insert a minimum orthogonal bounding rectangle for rectangle T and L, the rectangle is like
this (J is the new rectangle):
J
Insert the bounding rectangle into the R tree, the process would be as follows. Because for R-tree,
it will try to minimize the area, so it the search would go to Q->Z (Q has less enlargement than P
to include new rectangle). Because the child of entry Z is full, we have to split the node which
contains F and L. In this case, the split will continue to the root node. So the final result might be
as follows. (Some new nodes are added)
R
R’
P
W
B
T
Q
X
Y
H
N
S
K
Z’
J
F
Z
L
R+-tree:
J
R+-tree insert this new bounding rectangle, it will overlap all the existing bounding rectangle.
Therefore, if we insert this one to index, we have to split all the leaf nodes and deal with the
overflow. The insert result is as follows.
P
R
W
B
T
J
W’
R’
X
H
Q
N
M
X’
J
Y
N
S
M’
Y’
Z
J
F L
Z’
J
Q 6.4 : Revisit the first problem under chapter 5. Name efficient data-structure and access
methods for problems, which can be solved algorithmically.
1. Geo-locate all human settlements e.g. tents (or usable roads) a few days after Haiti
earthquake, given an aerial image (e.g. see examples: 1 , 2 ) a few days after Jan. 2010
earthquake.
Can’t solve algorithmically
2. Given a digital satellite image, create an object based model for water bodies including
wells (points), streams (linestring) and lakes (polygons).
Note: Students interested in the state of the art on such problem, may find a recent
Textbook section 5.6 titled vectorization and rasterization (pp. 207-211) interesting.
Freeman chain coding, Run length encoding, Region Quadtree
3. Given a news article (e.g. those from Google News), photograph, or video-clip, identify
the geographic location it is describing.
Note: Students interested in the state of the art on such problems, may find a recent
New York Times article interesting.
Can’t solve algorithmically
4. Find the elevation of a given point of interest (POI), given a regular tessellation based
representation of elevation field defined over the USA. For simplicity, use square based
tesselation of a Euclidean plane. Assume the availability of a geo-coding service to
convert POI to grid row and column. For simplicity, focus on non-nested tessellations.
Fixed grid, Point Quadtree, 2D tree, R-tree
5. Revisit the previous problem using regular triangular tesselation. List your assumptions
about the geo-coding service.
R-tree, QTM
6. Revisit the previous problem using irregular triangular tesselation. List your assumptions
about the geo-coding service.
R-tree, QTM
7. Given postal addresses of hotels, determine the hotel closest to a specified point of
interest (POI), e.g. the Mall of America. Use Euclidean space and straight-line distance for
simplicity. Assume the availability of a geo-coding service to convert postal addresses to
geographic point-locations.
R-tree, R+-tree
8. Revisit the previous problem using Network space and network-distances. Assume
roadmaps are represented as a graph using road-intersections as nodes and
road-segments connecting adjacent intersections as edges. Also available is a a
geo-coding service to place hotels and POIs to nearest road-intersection (nodes).
PM Quadtree, Adjacency list
9. Given a graph representation of a road-network (or electricity distribution network),
determine if it is connected.
PM Quadtree, Adjacency list