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This is a question present in Introduction to Algos by Cormen based on the topic of finding closest pair of points where Y' belongs to the vertical strip containing points which are at least some "delta" distance far away from a line "l". d is the minimum distance between any pair of point computed during the divide and conquer phase. P is the set of points, PL is the left set of points after the divide similarly PR is the right set of points.

Professor Williams comes up with a scheme that allows the closest-pair algorithm to check only 5 points following each point in array Y'. The idea is always to place points on line l into set PL. Then, there cannot be pairs of coincident points on line l with one point in PL and one in PR. Thus, at most 6 points can reside on the dx2d rectangle. What is the flaw in this algorithm?

karan patel
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user3350092
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    We can't read your mind and I have not been present on this lecture. I have no idea what Y' is and what are PL and PR. You have not even mentioned which algorithm are you talking about. It is not possible anyone could help you with that little information. – Ivaylo Strandjev Feb 25 '14 at 08:35

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First intuition: using this strategy, you can fail to split the point set into balanced subsets, compromising the linlog behavior (imagine ALL points on a vertical).