Abstract
This article presents an algorithm that solves the 3SUM problem for n real numbers in O (( n 2 / log 2 n )(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.
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