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Covering a Triangle with Disks Centered on its Boundary

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Abstract

Let P be a triangle and D1,D2 be disks centered on the boundary of P with radii r1, Extra close brace or missing open bracer}_{2}r}_{2}. The disks are chosen so that D1 D2 covers P and r1 + r2 is minimized. We show that an optimal covering must exist with r2 = 0. In such a single disk covering, D1 is always located on the longest side of P. The exact location and and size depend on the angles of P; we provide a complete characterization and then generalize it to convex polygons. We show that the minimum covering disk can be determined in O(n) time for a convex polygon with n sides. However, it is open for n 4 whether there is always a single disk covering that is optimal.

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1991-11

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR91-1242

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technical report

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