Some Geometric Lower Bounds
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چکیده
Dobkin and Lipton introduced the connected components argument to prove lower bounds in the linear decision tree model for membership problems, for example the element uniqueness problem. In this paper we apply the same idea to obtain lower bound statements for a variety of problems, each having the avor of element uniqueness. In fact one of these problems is a parametric version of element uniqueness which asks, given n inputs a1; : : : ; an and a query x 0, whether there is a pair of inputs satisfying jai ajj = x; the case x = 0 IS element uniqueness. Then we apply some of these results to establish the fact that \search can be easier than uniqueness"; speci cally we give two examples (one is the planar ham-sandwich cut) where nding or constructing a geometric object known to exist is less complex than answering the question about whether that object is unique. Finally we apply some of these results, along with a reduction argument, to get a nontrivial lower bound for the complexity of the least median of squares regression problem in the plane.
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تاریخ انتشار 1995