Computing contour trees in all dimensions

We show that contour trees can be computed in all dimensions by a simple algorithm that merges two trees. Our algorithm extends, simplifies, and improves work of S. P. Tarasov and M. N. Vyalyi [Construction of contour trees in 3D in O(nlogn) steps. In Proc. 14th Annu. ACM Sympos. on Comput. Geom., 68-75 (1998)] and of M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci and D. Schikore [Contour trees and small seed sets for isosurface traversal. In Proc. 13th Annu, ACM Sympos. Comput. Geom., 212-220 (1997)]