Lower Bound for Randomized Linear Decision Trees Recognising a Union of Hyperplanes in a Generic Position

Authors:
Dima Grigoriev;Marek Karpinski
Affiliations:
-;-
Venue:
Lower Bound for Randomized Linear Decision Trees Recognising a Union of Hyperplanes in a Generic Position
Year:
1994

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Abstract

Let $L$ be a union of hyperplanes with $s$ vertices. We prove that the runtime of a probabilistic linear search tree recognizing membership to $L$ is at least $\Omega\,(\log s)$, provided that $L$ satisfies a certain condition which could be treated as a generic position. A more general statement, namely without the condition, was claimed by F.~Meyer auf der Heide \cite{1}, but the proof contained a mistake.