ABSTRACT
Trees arise in many seemingly unrelated disciplines, including probability, chemistry, and computer science. The examples in this chapter provides context for the interest in trees, but are in no way comprehensive in terms of the applications of trees. After which, one can discusses optimal trees and how to find them. Similar to Dijkstra's Algorithm, Kruskal's Algorithm is fairly modern, first published in 1956. Joseph Kruskal was an American mathematician best known for his work in statistics and computer science. Prim's Algorithm contrasts from Kruskal's in that the structure obtained in each step is itself a tree. By the end of the process, a spanning tree will be found. Both minimum spanning tree algorithms described in this chapter are efficient and optimal, and result in roughly the same computation requirements. It should be noted that many other algorithms exist and the study of minimum spanning trees did not originate with Kruskal and Prim.
