All Approximating Segments for a Sequence of Points
نویسندگان
چکیده
In this paper, we consider the problem of approximating a sequence of n points by a line segment in such a way that the distance of each point from this segment is not greater than a given constant. Furthermore, the distance between the first(last) input point and the start(end)-point of the approximating segment must not be greater than the given constant. This is a sub-problem in solving unrestricted line simplification and minimum-link path problems. We propose an O(n log n) algorithm for computing a representation of these segments and we prove that the lower time complexity of finding all such segments (in a specific representation) is Ω(n log n) on the algebraic computation tree model which means that our algorithm is optimal.
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تاریخ انتشار 2014