Abstract
Given a set of circles C e lc1, …, cnr on the Euclidean plane with centers l(a1, b1), …, (an, bn)r and radii lr1, …, rnr, the smallest enclosing circle (of fixed circles) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment.
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