Energy-efficient fast delivery by mobile agents

Abstract

We consider the problem of collaboratively delivering a package from a specified source node s to a designated target node t in an undirected graph G = (V, E), using k mobile agents. Each agent i starts at time 0 at a node pi and can move along edges subject to two parameters: Its weight wi, which denotes the rate of energy consumption while travelling, and its velocity vi, which defines the speed with which agent i can travel. We are interested in operating the agents such that we minimize the total energy consumption E and the delivery time T (time when the package arrives at t). Specifically, we are after a schedule of the agents that lexicographically minimizes the tuple (E, T). We show that this problem can be solved in polynomial time O(k|V |2 + APSP), where O(APSP) denotes the running time of an all-pair shortest-paths algorithm. This completes previous research which shows that minimizing only E or only T is polynomial-time solvable [6, 7], while minimizing a convex combination of E and T, or lexicographically minimizing the tuple (T, E) are both NP-hard [7].