More Logarithmic-factor Speedups for 3SUM, (median,+)-convolution, and Some Geometric 3SUM-hard Problems

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1 total messages Started by unknown Fri, 15 Nov 2019 01:00

#454

Author: unknown
Date: Fri, 15 Nov 2019 01:00

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Timothy M. Chan<br /><br />This article presents an algorithm that solves the 3SUM problem for n real numbers in O((n2/ log2n)(log log n)O(1)) time, improving previous solutions by about a logarithmic factor. Our framework for shaving off two logarithmic factors can be applied to other problems, such as (median,+)-convolution/matrix multiplication and algebraic generalizations of 3SUM. This work also obtains the first subquadratic results on some 3SUM-hard problems in computational geometry, for example, deciding whether (the interiors of) a constant number of simple polygons have a common intersection.
<p><a href="http://dl.acm.org/citation.cfm?id363541">Link</a>

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