Ruminations on Tarjan's Union-Find Algorithm and Connected Operators

This papers presents a comprehensive and general form of the Tarjan’s unionfind algorithm dedicated to connected operators. An interesting feature of this form is to introduce the notion of separated domains. The properties of this form and its flexibility are discussed and highlighted with examples. In particular, we give clues to handle correctly the constraint of domain-disjointness preservation and, as a consequence, we show how we can rely on “union-find” to obtain algorithms for self-dual filters approaches and levelings with a marker function.