eldavojohn writes: After 65 years Paul Erdos' combinatorial problem has been solved by Indiana University professor Nets Hawk Katz. The problem involved determining the minimum number of distinct distances between any finite set of points in a plane and its applications range from drug development to robot motion planning to computer graphics. You can find a description of the problem here and the prepublication of the paper on arxiv. The researchers used the existing work on the problem and included two new ideas of their own like using the polynomial ham sandwich theorem to reach a solution that warranted at least half of Erdos' $500 reward posted for solving this problem way back in 1935.
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