We revisit classical problems about searching in totally monotone and Monge matrices, which have many applications in computational geometry and other areas. We present a number of new results, including the following:
We revisit classical problems about searching in totally monotone matrices, which have many applications in computational geometry and other areas. In a companion paper, we gave new (near-)linear-time algorithms for a number of such problems. In the present paper, we describe new subquadratic results for more basic problems, including the following:
These matrix searching problems are intimately related to problems about arrangements of pseudo-lines. In particular, our selection algorithm implies an O(n^{4/3} polylog n) algorithm for computing incidences between n points and n pseudo-lines in the plane. This improves, extends, and simplifies a previous method by Agarwal and Sharir [SODA'02].
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