CPS 296: Design and Analysis of Algorithms with Applications in GIS

Course Synopsis

The course is likely to contain a subset of the following topics (what has really been going on can be seen here):

1. Introduction to GIS

2. Geographic information models and representation

• Maps:
  - Raster and vector models.
• Digital elevation models (DEMs):
  - Grid
  - Contour line
  - Triangulated irregular networks (TINs): Storage, access, traversal, conversion from point, grid or contour line to TIN representation.

3. Data structures for GIS

• Internal:
  - Quad tree, point location and range searching structures.
• External:
  - B-tree, R-trees, grid file, k-d B tree, space filling curves.
• Worst case I/O efficient (2d range searching) structures:
  - Path caching, external interval tree, XP tree, metablock tree, P-range tree.

4. Computation on Terrains: (TIN computation)

• Contour line computation.
• Topographical features, classification, drainage networks, ...
• Visualization:
  - Perspective view (depth order for TINs).
  - Multi resolution models.

5. External memory algorithms with applications in GIS

• Sorting (merging, distribution).
• Buffer technique:
  - Buffer tree, external buffered segment tree.
• Use of parallel disks.
• Distribution sweeping:
  - Orthogonal line segment intersection, all nearest neighbors, batched range searching.
• External fractional cascading and batched filtering:
  - Segment sorting, batched planar point location, trapezoid decomposition, polygon triangulation.
• Contour lines computation revisited:
  - External list ranking
  - External graph blocking.

6. Computation on maps/map presentation

• Map overlay
  - Red/blue line segment intersection (internal and external).
  - Other algorithms.
• Map generalization
  - Line simplification.
• Label placement
• Polygon/polyline intersection.
• Buffer computation.

7. Implementation of GIS algorithms

• TPIE
• CGAL/LEDA
• Precision and robustness