volume 31, issue 1, P3-16 2004
DOI: 10.1007/s00454-003-2946-1
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Abstract: We define a close variant of line range searching over the reals and prove that its arithmetic complexity is (n log n) if field operations are allowed and (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 (n 1+c ) arithmetic operations, for some constant c > 0.

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