Identifying loops using DJ graphs

Loop identification is a necessary step in loop transformations for high-performance architectures. One classical technique for detecting loops is Tarjan's interval-finding algorithm. The intervals identified by Tarjan's method are single-entry, strongly connected subgraphs that closely reflect a program's loop structure. We present a simple algorithm for identifying both reducible and irreducible loops using DJ graphs. Our method is a generalization of Tarjan's method, as it identifies nested intervals (or loops) even in the presence of irreducibility.