Context-aware multi-stage routing

In context-aware route planning, a set of agents has to plan routes on a common infrastructure and each agent has to plan a conflict-free route from a source to a destination without invalidating plans made by other agents. The existence of such a conflict-free set of plans can be ensured if each agent is allowed to reserve time slots on the infrastructure resources it intends to use. In the multi-stage variant of the context-aware routing problem, each agent has a sequence of destination locations it must visit. A naive approach to solve the multi-stage variant is to make context-aware route plans between every two subsequent locations in the sequence, and then to concatenate these plans together. It can easily be shown, however, that this concatenation approach cannot guarantee that a multi-stage plan (if it exists) can always be found, and even if it is found, then it need not be optimal. Therefore, we present a new polynomial-time algorithm for the multi-stage routing problem that always returns the optimal (shortest-time) route for a single agent, given a set of reservations made by previous agents, thus providing a set of Pareto-optimal route plans. Obviously, the need for such a dedicated multi-stage routing algorithm depends on the frequency with which the concatenation approach fails to find a plan, or finds a rather inefficient one. Our experiments show that, given a set of reservations from 200 agents, the concatenation approach fails to find a solution in more than 50% of the cases, for random visiting sequences of six locations or more. However, if the concatenation approach does find a solution, its plan quality is often close to that of an optimal solution.