Timothy M. Chan's Publications: Matrix searching


(Near-)linear-time randomized algorithms for row minima in Monge partial matrices and related problems

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:


Near-optimal randomized algorithms for selection in totally monotone matrices

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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Timothy Chan (Last updated Nov 2020)