5. Acknowledgments 4. the Algorithm 3. Geodesic Circuits and Separability of Polygons 2. Geodesic Paths and Relative Convex Hulls on Separating Two Simple Polygons by a Single Translation*

Let P and Q be two disjoint simple polygons having n sides each. We present an al-gorithm which determines whether Q can be moved by a single translation to a posi-tion sufficiently far from P, and which produces all such motions if they exist. The al-gorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sidedpolygon. Since Tarjan and Van Wyk have recently shown that t(n) = O(n log log n)this improves the previous best result for this problem which was O(n log n) even af-ter triangulation.