TY - GEN
T1 - More logarithmic-factor speedups for 3SUM, (median,+)-convolution, and some geometric 3SUM-hard problems
AU - Chan, Timothy M.
N1 - Publisher Copyright:
© Copyright 2018 by SIAM.
PY - 2018
Y1 - 2018
N2 - We present an algorithm that solves the 3SUM problem for n real numbers in O((n2= log2 n)(log log n)O(1)) time, improving previous solutions by about a logarithmic factor. Our framework for shaving o two logarithmic factors can be applied to other problems, such as (median,+)convolution/matrix multiplication and algebraic generalizations of 3SUM. We also obtain 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.
AB - We present an algorithm that solves the 3SUM problem for n real numbers in O((n2= log2 n)(log log n)O(1)) time, improving previous solutions by about a logarithmic factor. Our framework for shaving o two logarithmic factors can be applied to other problems, such as (median,+)convolution/matrix multiplication and algebraic generalizations of 3SUM. We also obtain 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.
UR - http://www.scopus.com/inward/record.url?scp=85045537491&partnerID=8YFLogxK
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U2 - 10.1137/1.9781611975031.57
DO - 10.1137/1.9781611975031.57
M3 - Conference contribution
AN - SCOPUS:85045537491
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 881
EP - 897
BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
A2 - Czumaj, Artur
PB - Association for Computing Machinery
T2 - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
Y2 - 7 January 2018 through 10 January 2018
ER -