Algorithms, Probability, and Computing Solutions Kw42 Hs14 General Rules for Solving Exercises Solution 1: Farthest Point Voronoi Diagrams
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چکیده
(a) If one wants to de ne the locus where p is further away than all other points, i.e., strictly the farthest point, consider the following: As h(p, p ) := {x 2 R | d(x, p) < d(x, p )} denotes the open halfplane of all points that are strictly closer to p than to p , h(p , p) is the open halfplane on the other side of the bisector b(p, p ) of p and p that contains all points strictly farther away from p than from p. The intersection of all such open halfplanes for all p 2 S, p 6= p, is thus the set of points that is strictly farther away from p than from any other point in S, and hence we have
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Algorithms, Probability, and Computing Solutions Kw39 Hs14 General Rules for Solving Exercises
(a) This is false. What is true is that uniform choice of π induces the regular search tree distribution for Tπ. But the other way round, the implication does not hold. There are many other distributions on the permutations that induce the same distribution on the trees. Indeed, we know that many trees arise from several di erent permutations and among those permutations yielding the same tree,...
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