Dijkstra Graphs

TL;DR

This paper introduces Dijkstra Graphs to model structured programs and presents efficient linear-time algorithms for recognizing such graphs and testing their isomorphism, aiding code analysis.

Contribution

It defines Dijkstra Graphs and provides the first linear-time algorithms for their recognition and isomorphism testing, advancing structured programming analysis.

Findings

Linear-time recognition algorithm for Dijkstra Graphs

Linear-time isomorphism algorithm for Dijkstra Graphs

Potential applications in code similarity analysis

Abstract

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 structure that is desirable in many aspects. While much has been written about structured programming, an important issue has been left unanswered: given an arbitrary, compiled 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 the classical concept of structured programming, as described by Dijkstra. By employing a graph model and graph-theoretic techniques, we formulate an efficient algorithm for answering this question. To do so, we first introduce the class of graphs which correspond to structured programs, which we call Dijkstra Graphs. Our problem then becomes the recognition of such graphs, for which we present a greedy $O(n)$-time algorithm. Furthermore, we describe an isomorphism algorithm for Dijkstra graphs, whose complexity is also linear in the number of vertices of the graph. Both the recognition and isomorphism algorithms have potential important applications, such as in code similarity analysis.