17 On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem (1956)

This paper by mathematician Joseph Kruskal (1928-2010) marks an early step along a path from operations research—a field that had flourished during the 1940s in response to the need to solve a variety of commercial, military, and logistical problems—to computer science, which some define as the study of algorithms. The particular algorithm presented here as Construction A, now known as Kruskal's algorithm, finds the minimum-cost spanning tree in an undirected graph by growing a forest, adding edges one by one from shortest to longest, not including any edge that would create a cycle. Borûvka (1926), to which the paper refers in its first sentence, is probably the first published algorithm for this problem, dating from a time before the basic vocabulary of graph theory had been formalized. In that paper, the Czech mathematician Otakar Borûvka had solved the problem of finding the most efficient electrical network for Moravia, a region of what is now the Czech Republic.