Affiliation:
1. University of Illinois at Urbana-Champaign, Urbana, IL, USA
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
12 articles.
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