  Interval routing is a space efficient method to realize a distributed routing
function. In this paper we show that every circular-arc graph allows a shortest
path strict 2-interval routing scheme, i.e., by introducing a global order on
the vertices and assigning at most two (strict) intervals in this order to the
ends of every edge allows to depict a routing function that implies exclusively
shortest paths. Since circular-arc graphs do not allow shortest path 1-interval
routing schemes in general, the result implies that the class of circular-arc
graphs has strict compactness 2, which was a hitherto open question.
Additionally, we show that the constructed 2-interval routing scheme is a
1-interval routing scheme with at most one additional interval assigned at each
vertex and we an outline algorithm to calculate the routing scheme for
circular-arc graphs in O(n^2) time, where n is the number of vertices.
