Package Delivery Using Drones with Restricted Movement Areas

TL;DR

This paper investigates drone package delivery within restricted movement areas, providing complexity results and algorithms for minimizing delivery time and energy consumption across various graph structures.

Contribution

It introduces new complexity results and approximation algorithms for delivery problems with movement restrictions, including special cases like paths and trees.

Findings

Strong inapproximability for general graphs and algorithms for delivery time.

NP-hardness and approximation results for energy consumption.

Optimal algorithms for trees with uniform drone parameters.

Abstract

For the problem of delivering a package from a source node to a destination node in a graph using a set of drones, we study the setting where the movements of each drone are restricted to a certain subgraph of the given graph. We consider the objectives of minimizing the delivery time (problem DDT) and of minimizing the total energy consumption (problem DDC). For general graphs, we show a strong inapproximability result and a matching approximation algorithm for DDT as well as NP-hardness and a 2-approximation algorithm for DDC. For the special case of a path, we show that DDT is NP-hard if the drones have different speeds. For trees, we give optimal algorithms under the assumption that all drones have the same speed or the same energy consumption rate. The results for trees extend to arbitrary graphs if the subgraph of each drone is isometric.