Hmwk1 - having these points on its boundary Analyze the...

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COT5520 Computational Geometry Fall 2003 Homework Assignment # 1 Due: September 8, 2003 1. Given a doubly connected edge list (DCEL) data structure as described in Berg et al (and also presented in the class), write an algorithm to find the edges enclosing a given face k. Assume that the planar graph is connected (but there my be holes). Call this FACE(k) algorithm. Analyze the time and storage complexity of your algorithm. Although a C or C++ implementation is not required, you might just want to write one for future use and test your algorithm with some sample data. 2. Given N points in a plane, design an algorithm to construct a simple polygon
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Unformatted text preview: having these points on its boundary. Analyze the complexity of your algorithm. 3. Let P be a non-convex polygon. Describe an algorithm that computes the convex hull of P in O(n). 4. Using Euler’s formula as a starting point, prove the following inequalities for a planar graph with the additional property that each vertex has degree greater than or equal to 3; a. e v 3 2 ≤ b. 6 3-≤ f e c. e f 3 2 ≤ d. 6 3-≤ v e e. 4 2-≤ f v f. 4 2-≤ v f Also prove that if a planar graph is triangulated (that is every face is a triangle. Note in this case some vertices may have degree less than 3) then 6 3-= v e ....
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