Dijkstra graphs

We revisit a concept that has been central in some early stages of computer science, that of structured programming: a set of rules that an algorithm must follow in order to acquire a certain desirable structure. While much has been written about structured programming, an important issue has been left unanswered: given an arbitrary program, describe an algorithm to decide whether or not it is structured, that is, whether it conforms to the stated principles of structured programming. We refer to a classical concept of structured programming, as described by Dijkstra. By employing graph theoretic techniques, we formulate an efficient algorithm for answering this question. First, we introduce the class of graphs which correspond to structured programs, which we call Dijkstra Graphs. Then we present a greedy O(n)-time algorithm for recognizing such graphs. Furthermore, we describe an isomorphism algorithm for Dijkstra graphs, whose complexity is also linear in the number of vertices of the graph.