The power of nonmonotonicity in geometric searching

Authors:
Bernard Chazelle
Affiliations:
Princeton University and NEC Research Institute
Venue:
Proceedings of the eighteenth annual symposium on Computational geometry
Year:
2002

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Abstract

(MATH) We define a close variant of line range searching over the reals and prove that its arithmetic complexity is $\Theta(n log n) if field operations are allowed and $\Theta(n 3/2) if only additions are. This provides the first nontrivial separation between the monotone and nonmonotone complexity of a range searching problem. The result puts into question the widely held belief that range searching for nonisothetic shapes typically requires &OHgr;(n 1+c) arithmetic operations, for some constant c0.