
Computational Geometry: An Introduction Through Randomized Algorithms, 1/e
Ketan Mulmuley, The University of Chicago Published February, 1998 by Prentice Hall Engineering/Science/Mathematics
 
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Quicksort. Another view of quicksort. Randomized binary trees. Skip lists. 2. What Is Computational Geometry? Range queries. Arrangements. Trapezoidal decompositions. Convex polytopes. Voronoi diagrams. Hidden surface removal. Numerical precision and degeneracies. Early deterministic algorithms. Deterministic vs. randomized algorithms. The model of randomness. 3. Incremental Algorithms. Trapezoidal decompositions. Convex polytopes. Voronoi diagrams. Configuration spaces. Tail estimates. 4. Dynamic Algorithms. trapezoidal decompositions. Voronoi diagrams. History and configuration spaces. Rebuilding history. Deletions in history. Dynamic shuffling. 5. Random Sampling. Configuration spaces with bounded valence. Topdown sampling. Bottomup sampling. Dynamic sampling. Average conflict size. More dynamic algorithms. Range spaces and II. APPLICATIONS.
Incremental construction. Zone Theorem. Canonical triangulations. Point location and ray shooting. Point location and range queries. 7. Convex Polytopes. Linear Programming. The number of faces. Incremental construction. The expected structural and conflict change. Dynamic maintenance. Voronoi diagrams. Search problems. Levels and Voronoi diagrams of order k. 8. Range Search. Orthogonal intersection search. Nonintersecting segments in the plane. Dynamic point location. Simplex range search. Halfspace range queries. Decomposable search problems. Parametric search. 9. Computer Graphics. Hidden surface removal. Binary Space Partitions. Moving viewpoint. 10. How Crucial Is Randomness? Pseudorandom sources. Derandomization. Appendix: Tail Estimates. Chernoff's technique. Chebychev's technique. Bibliography. Index.
