Speeding Up Constrained Path Solvers with a Reachability Propagator

Constrained path problems have to do with finding paths in graphs subject to constraints. One way of constraining the graph is by enforcing reachability on nodes. For instance, it may be required that a node reaches a particular set of nodes by respecting some restrictions like visiting a particular set of nodes or edges and using less than a certain amount of resources. The reachability constraints of this paper were suggested by a practical problem regarding mission planning in the context of an industrial project. We deal with this problem by using concurrent constraint programming where the problem is solved by interleaving Propagation and Labeling. In this paper, we define a propagator which we call Reachability that implements a generalized reachability constraint on a directed graph g. Given a source node source in g, we can identify three parts in the Reachability constraint: (1) the relation between each node of g and the set of nodes that it reaches, (2) the association of each pair of nodes 〈source, i〉 with its set of cut nodes, and (3) the association of each pair of nodes 〈source, i〉 with its set of bridges. We show the effectiveness of our Reachability propagator by applying it to the Simple Path problem with mandatory nodes. We do an experimental evaluation of Reachability that shows that it provides strong pruning, obtaining solutions with very little search. Furthermore, we show that Reachability is also useful for defining a good labeling strategy and dealing with ordering constraints among mandatory nodes. These experimental results give evidence that Reachability is a useful primitive for solving constrained path problems over graphs.