Separating Bichromatic Point Sets by Right Triangles
Subject Areas : electrical and computer engineering
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Abstract :
Separating colored point sets is an interesting problem in computational geometry with application in machine learning and pattern recognition. In this problem, we are given a geometric shape C and two point sets P and Q of total size n as red and blue points, respectively. Now, we must separate red and blue points by this shape such that all the blue points lie inside it and all the red points lie outside it. In the previous work, we have some algorithms for rectangle and wedge separability but we do not have any algorithm for separating by a triangle and separating by a triangle with a fixed angle such as right triangle. In this paper, we present an efficient algorithm for right triangle seprability. In this algorithm, we use sweep line technique and introduce some events and process them. So, we can report all separating right triangles in O(nlog n) time.
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