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\indent In this paper we present efficient algorithms for counting intersections in a collection of circles or circular arcs. We present a randomized algorithm to count intersections in a collection of $n$ circles whose expected running time is $O(n^{3/2+\epsilon})$, for any $\epsilon < 0.$ We also develop another randomized algorithm to count intersections in a set of $n$ circular arcs whose expected running time is $O(n^{5/3+\epsilon})$, for any $\epsilon < 0.$ If all arcs have the same radius, the (expected) running time can be improved to $O(n^{3/2+\epsilon})$, for any $\epsilon < 0$.

Counting circular arc intersections