Open Problems: Open Problems from CCCG 2005
نویسندگان
چکیده
Consider the following special case of planar point location: preprocess k sets of lines, where each set consists of parallel lines, to support queries of the form “given a point p, what is the line immediately above or below p?” What is the fastest possible query time as a function of k and the total number n of lines? In other words, the n given lines have k distinct orientations. See Figure 1. In this problem, the data structure must use O(n polylog n) space, preventing us from simply constructing the arrangement of Θ(n2) cells and preprocessing with standard point location. An obvious O(k log n) algorithm—search for p in each set of parallel lines separately, and then combine the answers—is so far the best solution to this problem.
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