On a Class of 3SUM-HARD problems in Computational Geometry | Cutting a polygon with a line

On a Class of 3SUM-HARD problems in Computational Geometry : Cutting a polygon with a line

Taschenbuch. Condición: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Given a simple polygon P and an integer K 1, wewant to compute the set ofstraight lines in the Cartesian plane that cut thispolygon into exactly K simplepolygons. We call this set of lines a K-separator andcall this problem the K-separatorproblem.We present an algorithm that finds the K-separatorsof an n-vertex simple polygon,for all K 0, in O(n2) total time.We prove that the decision problem given an integer K 2 and an edge of thepolygon, is there a line through this edge that cutsthe polygon in exactly K pieces , is3SUM-HARD. For the special case when K = 2, we showthat the decision problemcan be solved in O(n log(n)) time.Several other complexity results may be obtained. Wesuspect that the problemof finding the cell of maximum depth is also3SUM-hard, and as a corollary theproblem of identifying the line that cuts the polygonin the maximum possible numberof pieces is also 3SUM-hard. Nº de ref. del artículo: 9783639158373

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