Algorithms · Divide-and-conquer algorithms
Two disjoint color classes contain r≥1 red and b≥1 blue planar points
Problem
Two disjoint color classes contain \(r\ge1\) red and \(b\ge1\) blue planar points. Find a minimum-distance opposite-color pair, breaking ties lexicographically. Design an \(O((r+b)\log(r+b))\)-time divide-and-conquer algorithm, prove the cross-partition candidate bound, and state auxiliary space.
Hint
** Same-color points can cluster, so the ordinary bichromatic strip argument needs a different sparse structure.
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