Unformatted text preview: , where d is a constant. Show that the convex hull of S can be obtained in linear time. 5. Design an efficient algorithm to solve the following problem: Given n boy robots and n girl robots, whose positions are specified by points in the plane, such that the boy robots are separated from the girl robots by a vertical line. Find a matching of the boys with the girls by straight linesegments so that no two segments intersect. Intuitively, this corresponds to the paths the boys will have to make to pick a girl to go square dancing with. If more than one pair of boys and girls become collinear, their paths may have to overlap, but what will be a gentleman’s etiquette to avoid collision? What is the complexity of your algorithm? (Hint: Use convex Hulls)....
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 Spring '11
 Mukherjee
 Geometry, #, Convex hull, doubly connected edge

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