The JS-graphs of Join and Split Trees
Suyi Wang, Yusu Wang, Rephael Wenger · 2014
Let f be a continuous function defined on a topological space. As we increase the function value, connected components in the level set of f appear, disappear, merge, or split, and the Reeb graph tracks these changes. The join and split trees of f track the changes of connected components in the sublevel and superlevel set respectively. If the Reeb graph is loop-free, then it is a tree called the contour tree. Given a piecewise linear function f defined on a simplicial complex K, Carr, Snoeyink and Axen proposed a simple and elegant algorithm to compute the contour tree of f by "merging" its join and split trees in near-linear time.