Geometric Retrieval Problems

Cover Geometric Retrieval Problems
Geometric Retrieval Problems
Richard Cole
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Flight simulation graphics). It is usually relatively easy to determine the preprocessing time for our algoritlims; typically, it is 0{n. G{n)), where g{n) is the space complexity. We use the 'locate run time' in the sense of [W] for our qtiery time: it is the time to locate the first object in the answer, where it is assumed each additional object can be output in constant time.
Our initial motivation was the triangle retr:e\'al problem. It can be used to solve the polygon retrieval problem, b
...y decomposing the polygon into disjomt triangles.^ [EBOil] obtained a space- time bound of 0(n', logn) for this problem; they ware cpnsidepug the more general problem of polygon intersection but the space complexity of triangle retrieval jdominatr: in their solution. They posed the challenge of reducing this space con^lexity. , We stiow that the space-time com- plexity can be drastically reduced to (Xn-^^'. LognlogCl/c)) for any e>0; we also obtain a solution with complexity 0(n-, lognloglogn). Both solutions admit extensions to higher dimensions.

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