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Hopcroft's Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees
[article]
2021
arXiv
pre-print
We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O(n^4/3) time, which matches the conjectured lower bound and improves the best previous time bound of n^4/32^O(log^*n) obtained almost 30 years ago by Matoušek. We describe two interesting and different ways to achieve the result: the first is randomized
arXiv:2111.03744v1
fatcat:3emz4diddvgupbqzvs3ez6cr2e