CPS 296. Advanced Topics in Computer Science

Summary of Lectures and list of Material.

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Summary of lectures:

Lec.	Date	Topics	Reading
1	Jan. 17	Practical introduction to course. Introduction to GIS: What is a GIS, examples of use of GIS, GIS as a research field.	GIS reader chapter 1, sec. 1.1-1.2 "Why GIS", GIS analysis with ARC-INFO ("How I analyzed the data in ARC-INFO")
2	Jan. 20	Introduction to GIS: Needs of a GIS, error handling, outline of course. Geographic information models and representation: Raster and vector maps (representation), DEMs (grid, contour line, TIN), TINs (storing).	GIS reader chapter 1, sec. 1.3-1.4 + chapter 2, sec. 2.1-2.3 DEM survey chapter 1 + chapter 2, sec. 2.1-2.3.1
3	Jan. 24	Geographic information models and representation: Traversing a TIN, access to a TIN, conversion from point to TIN (Delauney triangulation/Voronoi diagram).	DEM survey chapter 2, sec 2.3.2-2.4.1. CG Book chapter 7, sec. 7.1+ chapter 9, sec. 9.1-9.3
4	Jan. 27	Geographic information models and representation: Grid and contour line to TIN, mathematical computations on TINs.	CG Book chapter 9, sec. 9.4. DEM survey chapter 2, sec 2.4.2-2.6.2
5	Jan. 31	Internal data structures for GIS: Raster data: Quadtrees. Vector data (range searching): Point quadtrees, kd-trees, range trees.	GIS reader chapter 3, sec. 3.1.1 CG Book chapter 5, sec. 5.1-5.4 [Samet88]
6	Feb. 3	External data structures for GIS: B-trees, (a,b)-trees and their properties.	Mehlhorn1, pages 199-206 + 212-222
7	Feb. 7	External data structures for GIS: Survey of spatial data structures, grid files, R-trees and R-trees, spatial joins using R-trees.	Data structure survey [NHS84] [Guttman84], [BKSS90], [BKS93]
8	Feb. 10	External data structures for GIS: Worst-case efficient interval trees (on fixed endpoint set).	Thesis chapter 8.
9	Feb. 14	External data structures for GIS: Worst-case efficient interval (and segment trees), weight-balanced B-trees. Computation on terrains: Computing contour lines from a TIN.	Thesis chapter 8. DEM survey chapter 3, sec 3.1.
10	Feb. 17	External data structures for GIS: Worst-case efficient data structures for (two sided) 2d range searching: Path caching.	[RS94]
11	Feb. 21	External data structures for GIS: Worst-case efficient data structures for (two sided) 2d range searching: P-range tree.	[SR95]
-	Feb. 24	Cancelled
12	Feb. 28	Computation on Terrains: Classification, topographic features, drainage network.	DEM survey chapter 3, sec 3.2, 3.4, 3.5 and 3.6.
13	Mar. 3	Computation on Terrains: Visualization of terrains (TINs): Z-buffer algorithm, depth orders (for TINs), painters algorithm, "shadow maintanance" (for terrains - Reif & Sen algorithm), KOS algorithm.	DEM survey chapter 3, sec 3.4. Visualization slides. [RS88], sec I and III. [KOS92], [D94].
14	Mar. 7	External memory algorithms: I/O model, permuting (upper and lower bound), sorting (upper bound; merge and distribution sort).	[AV88] External survey sec. 1, 2 and 3.1-3.2.
15	Mar. 10	External memory algorithms: Sorting (lower bound), buffer tree (using basic tree to sort, external piority queue). Discussion of parallel disk model and of hierarchical models.	External survey sec. 3.3-3.4 Thesis chapter 6, sec 1-3.
16	Mar. 14	External memory algorithms: The orthogonal line segment intersection problem: range searching on buffer tree.	External survey sec. 4.1.2. Thesis chapter 6, sec 5.
-	Mar. 17	Spring Break
-	Mar. 21	Spring Break
17	Mar. 24	External memory algorithms: The orthogonal line segment intersection problem: distribution sweeping, experimental results. Other applications of distribution sweeping, discussion of lower bounds.	External survey sec. 4.1 [GTVV93] sec. 1-2.
-	Mar. 28	Cancelled
18	Mar. 31	Student talks: Rakesh: Sorting using D-disks. Pavan: Simplification Paul: Multi-resolution surface representation & compression.
19	Apr. 2	Student talks: Robert: Map labeling External memory algorithms: External list ranking, PRAM simulation.	Thesis chapter 4, sec. 4.1-4.2. (see also chapter 9, lemma 2) [CGGTVV95]
20	Apr. 4	TPIE Guest lecture by Darren Vengroff, University of Delaware.	External survey sec. 5. See also TPIE home page.
21	Apr. 7	External memory algorithms: The batched range searching problem: External buffered segment tree. The endpoint dominance (EPD)problem: Connection with batched planar point location, segment sorting, trapezoid decomposition, simple polygon triangulation.	External survey sec. 4.2 and 4.3.1. Thesis chapter 6, sec 6. Thesis chapter 7, sec. 1-2..2.
22	Apr. 11	External memory algorithms: Solution to EPD problem: Extended segment trees, external fractional cascading.	External survey sec. 4.3.2. Thesis chapter 7, sec. 2.3.
23	Apr. 14	External memory algorithms: Convex Hull computation. Map overlaying : Introduction: Network overlay, subdivision overlay (function and merging phase). Network overlay (red/blue line segment intersection): Overview of space partitioning and space ordering algorithms, trapezoid sweep algorithm, experimental results.	[GTVV93] sec. 6. External survey sec. 4.4 [ASBCDHZ94], [C94]
24	Apr. 18	Map overlayng: Network overlay: External-memory algorithm. Subdivision overlay: Overlaying general and simply connected subdivisions. Discussion of open problems.	External survey sec.4.3.3. Thesis chapter 7, sec. 3.1 CG Book chapter 2 (sec. 2.3). [FH95]
25	Apr. 21	Generalization: Overview of generalization, line simplification (Douglas-Peucker algorithm)	[W96] ,[HS92]
26	Apr. 25	Generalization: Line simplification (overview and Imai-Iri algorithm), issues in subdivision simplification. Terrain simplification.	[BKS95] sec 1-3 [AV97], sec 1-2 [HG95], sec 1-2

Covered material:

Geographic Information Systems. Reader for GIS course by Marc van Kreveld, University of Utrecht, 1995.

Chapter 1: Introduction (lecture 1 and 2).
Chapter 2: GIS Models and Representation (lecture 2).
Chapter 3: Data Structures for GIS (lecture 5 and 7).

"Why GIS" from Understanding GIS - the ARC/INFO method. rev. 6 for workstations, 1993.(lecture 1)
Digital Elevation Models: overview and selected TIN algorithms.
Lecture notes by Marc van Kreveld, Utricht University, for CISM Advanced School on Algorithmic foundation of GIS, August 1996.

Chapter 1: Introduction (lecture 2).
Chapter 2: Terrain models and representation (lecture 2, 3 and 4).
Chapter 3: The use of terrains (lecture 9, 12 and 13).

Computational Geometry by Example (draft of book version 0.1). M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf.

Chapter 2: Line Segment Intersection - Thematic Map Overlay (lecture 24).
Chapter 7, sec 7.1: Voronoi Diagrams (lecture 3).
Chapter 9, sec. 9.1-9.4: Delaunay Triangulations (lecture 3 and 4).
Chapter 5: Othogonal Range Searching (lecture 5).

An Overview of Quadtrees, Octrees and Related Hierarchical Data Structures. H. Samet, University of Maryland. (lecture 5).
In Theoretical Foundation of Computer Graphics and CAD, R.A. Earnshaw (Ed.), NATO ASI Series, Vol. F40, Springer-Verlag, 1988.
Data Structures and Algorithms 1: Sorting and Searching.
Kurt Mehlhorn, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1984.

Subset of Chapter III 5.2 on (a,b)-trees (pages 199-206 and 212-222) (lecture 6).

Spatial Data Structures: Concepts and design choices.
Lecture notes by Jurg Nievergelt and Peter Widmayer, ETH Zurich, for CISM Advanced School on Algorithmic foundation of GIS, August 1996. (lecture 7).
The Grid File: An Adaptable, Symmetric Mulitkey File Structure. J. Nievergelt, H. Hinterberger and K.C. Sevcik, ACM trans. on Database Systems, Vol. 9, No. 1, March 1984. (lecture 7).
R-Trees: A Dynamic Index Structure for Spatial Searching. A. Guttman. In Proc. ACM SIGMOD, 1984. (lecture 7).
The R*-tree: An Efficient and Robust Access Method for Points and Rectangles. N. Beckmann, H.-P. Kriegel, R. Schneider and B. Seeger. In Proc. ACM SIGMOD, 1990. (lecture 7).
Efficient Processing of Spatial Joins Using R-Trees. T. Brinkhoof, B. Seeger. In Proc. ACM SIGMOD, 1993. (lecture 7).
Efficient External-Memory Data Structures and Applications.
Lars Arge, PhD thesis, University of Aarhus, 1996. BRICS Dissertation Series DS-96-3.

Chapter 6: The Buffer Tree: A New Technique for Optimal I/O-Algorithms. Lars Arge (lecture 15, 16 and 21).
Chapter 8: Optimal Dynamic Interval Management in External Memory. Lars Arge and Jeff Vitter (lecture 8 and 9).
Chapter 4 (section 4.1-4.2): Graph Problems (lecture 19).
Chapter 7: External-Memory Algorithms for Processing Line Segments in Geographic Information Systems. Lars Arge, Darren Vengroff and Jeff Vitter (lecture 21, 22 and 24).

Path Caching: A Technique for Optimal External Searching. S. Ramaswamy and S. Subramanian. In Proc. ACM PODS, 1994 (appears also as Brown University, CS dept. technical report CS-94-27) (lecture 10).
The P-range Tree: A New Data Structure for Range Searching in Secondary Memory. S. Subramanian and S. Ramaswamy. In Proc. ACM-SIAM SODA, 1995 (lecture 11).
Visualization of TINs. Mark de Berg, Utrecht University. Slides from CISM Advanced School on Algorithmic foundation of GIS, August 1996 (lecture 13).
An Efficient Output-Sensitive Hidden-Surface Removal Algorithm and its Parallelization. J. Reif and S. Sen. In Proc. ACM Symp. on Computational Geometry, 1988 (lecture 13)
Efficient hidden surface removal for objects with small union size. M. J. Katz, M. H. Overmars and M. Sharir. Computational Geometry: Theory and Applications 2 (1992) 223-234 (lecture 13).
A Survey of Object-Space Hidden Surface Removal. S. E. Dorward. International Journal of Computational Geometry & Applications 4 (3), 1994, 235-362 (lecture 13).
The Input/Output Complexity of Sorting and Related Problems. A. Aggarwal and J. Vitter. CACM 31 (9), 1988 (lecture 14 and 15).
External-Memory Algorithms with Applications in Geographic Information Systems. L. Arge. In Algorithmic Foundations of GIS, eds. M. van Kreveld, J. Nievergelt, T. Roos and P. Widmayer, LNCS (subseries: tutorials), Springer-Verlag (to appear) (lecture 14, 15, 16, 17, 20, 21, 22 and 24).
External-Memory Computational Geometry. M. T. Goodrich, J.-J. Tsay, D. E. Vengroff and J. S. Vitter. In Proc. IEEE STOC, 1993 (lecture 17 and 23).
External-Memory Graph Algorithms. Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff and J. S. Vitter. In Proc. ACM-SIAM SODA, 1995 (lecture 19).
Further Comparison of Algorithms for Geometric Intersection Problems. D. S. Andrews et al. In Proc. 6'th International Symposium on Spatial Data Handling, 1994 (lecture 23).
A Simple Trapezoid Sweep Algorithm for Reporting Red/Blue Segment Intersections. T. M. Chan. In Proc. 6'th Canadian Conferance on Computational Geometry, CCCG, 1994 (lecture 23).
Overlaying simply connected planar subdivisions in linear time. U. Finke and K. H. Hinrichs. In Proc. 11'th ACM Symp. on Computational Geometry, 1995 (lecture 24).
Generalization of Spatial Data (Draft version d0.1). Lecture notes by Robert Weibel, University of Zurich, for CISM Advanced School on Algorithmic foundation of GIS, August 1996 (lecture 25).
Speeding Up the Douglas-Peucker Line-Simplification Algorithm. J. Hershberger and J. Snoeyink. In Proc. 5'th Int'l Symp. on Spatial Data Handling, 1992 (lecture 25).
A New Approach to Subdivision Simplification. M. de Berg, M. van Kreveld and S. Schirra. In Proc. AUTO-CARTO 12, 1995 (lecture 26).
Efficient Algorithms for Approximating Polygonal Chains. P. K. Agarwal and K. R. Varadarajan. In Proc. ACM Symp. on Computational Geometry, 1996 (lecture 26).
Fast Polygonal Approximation of Terrains and Height Fields. P. S. Heckbert and M. Garland. Carnegie Mellon University technical report CMU-CS-95-181, 1995 (lecture 26).

Extra material:

Digital Terrain Modelling. R. Weidel and M. Heller.
In Geographical Information Systems - Principles and Applications (Vol. 1) by D. J. Maguire, M. F. Goodchild and D. W. Rhind, 1991
Blocking for External Graph Searching. M. H. Nodine, M. T. Goodrich and J. S. Vitter. Algorithmica 16 (2), p. 181-214, 1996.

Lars Arge
Fri Apr 25, 1997