The minimum circle is more expensive to compute (for an irregular polygon) but that's O(n). Since the circle is smaller it will be no worse and maybe a good bit better for weeding out non-overlaps and the bonus that brings will depend entirely on the dataset being examined. Without seeing sample data, would you take the O(n) hit for an O(n2) gain? I probably would.
(I bet it's not)
It's a gamble either way. :-)
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