Minimum convex partition of a constrained point set
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We present two algorithms that compute constant factor approximations of a minimum convex partition of a set P of n points in the plane. The first algorithm is very simple and computes a 3-approximation in O(n logn) time. The second algorithm improves the approximation factor to $\frac{30}{11} O(n2) time. The claimed approximation factors are proved under the assumption that no three points in P are collinear. As a byproduct we obtain an improved combinatorial bound: there is always a convex partition of P with at most $\frac{15}{11}n -- \frac{24}{11}$ convex regions