Top-Down Analysis of Path Compression: Deriving the Inverse-Ackermann Bound Naturally (and Easily)
Path compression is used in a number of algorithms, most notably in various very natural solutions to the so-called Union-Find problem. This problem is basic and important enough to be covered in most introductory courses and textbooks on algorithms and data structures. However the performance analysis of the solutions is more often than not at best incomplete if not omitted altogether. Already the definition of the function α, the interesting constituent of the time bound, as a quasi inverse of the Ackermann function is complicated and not easy to understand.