  We present a graph-theoretical approach that can detect which equations of a
delay differential-algebraic equation (DDAE) need to be differentiated or
shifted to construct a solution of the DDAE. Our approach exploits the
observation that differentiation and shifting are very similar from a
structural point of view, which allows us to generalize the Pantelides
algorithm for differential-algebraic equations to the DDAE setting. The primary
tool for the extension is the introduction of equivalence classes in the graph
of the DDAE, which also allows us to derive a necessary and sufficient
criterion for the termination of the new algorithm.
