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Unformatted text preview: 2. Let S be a subdivision of complexity n , and let P be a set of m points. Give a plane sweep algorithm that computes for every point in P in which face of S it is contained. Show that your algorithm runs in time. ( ) ( ( ) m n m n O + + log ) 3. Prove or disprove: The dual graph of the triangulation of a monotone polygon is always a chain, that is, any node in this graph has degree at most two. 4. Give the pseudo-code of the algorithm to compute a 3-coloring of a triangulated simple polygon. The algorithm should run in linear time. 5. Show that if a polygon has O turn vertices, then the polygon triangulation algorithm, given in chapter 3 of Berg et al, can be made to run in O time. ( ) 1 ( ) n...
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- Summer '11