Distributed termination detection in reducible communication graphs

A distributed termination detection (DTD) algorithm is presented that can be superimposed upon a diffusing computation in which channels are unidirectional and the communication graph is reducible. A flow graph with the source node s is reducible if it can be transformed into a single node by repeatedly applying this operation: 1. Pick a node w not equal to s with a single incoming edge (v,w). 2. Remove node w and its outgoing edges, but for each outgoing edge (w,x) of w with x not equal to v, add an edge (v,x), if not present in the graph. The algorithm works even if channels are bidirectional and performs better than the algorithm of Chandrasekaran and Venkatesan (1990). The proposed algorithm works by passing tokens. It is started by the source node and the termination is detected by the exit node. It works if a channel exists from the exit to the source node, that is, if the graph is strongly connected. In that case, the exit node coincides with the source.