Implementing Union-Find Algorithm with Base SAS DATA Steps and Macro Functions

Union-Find algorithm is a classic algorithm used to form the union of disjoined sets and find connected components of a graph from a given set of vertices and edges. The algorithm is often used in data manipulations that involve graphs, trees, hierarchies, and linked networks. A tree data structure can be used to implement the algorithm. A SAS data set is a tuple data structure that is excellent for table manipulations, but cannot be directly applied for implementing Union-Find algorithm. In this paper, we will discuss the programming techniques that are available in Base SAS for the implementation of the Union-Find algorithm. We will explain how to implicitly represent graphs and trees using SAS arrays, and how to build hierarchical trees and perform queries on trees using SAS DATA steps and macro functions. We will also discuss the programming techniques that have been used to minimize average running time of the algorithm.