Parameterized Algorithms for the Drone Delivery Problem

2026-02-04

International Symposium on Algorithms and Computation

AI Summary

This study addresses the problem of coordinated delivery of multiple packages by heterogeneous agents—such as drones and trucks—operating within constrained movement regions, with the objective of minimizing total delivery time (DDT). By modeling the overlap of agents’ movement regions via an intersection graph, the work establishes for the first time that the DDT problem on path graphs admits no polynomial-time approximation algorithm unless P = NP. Introducing the treewidth of the intersection graph as a key parameter, the authors design the first fixed-parameter tractable (FPT) algorithm, running in time f(w)·poly(n,k) on path graphs and f(Δ,w)·poly(n,k) on general graphs, where w denotes treewidth and Δ the maximum degree. Moreover, when the intersection graph is a tree, they provide a polynomial-time exact algorithm.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Timely delivery and optimal routing remain fundamental challenges in the modern logistics industry. Building on prior work that considers single-package delivery across networks using multiple types of collaborative agents with restricted movement areas (e.g., drones or trucks), we examine the complexity of the problem under structural and operational constraints. Our focus is on minimizing total delivery time by coordinating agents that differ in speed and movement range across a graph. This problem formulation aligns with the recently proposed Drone Delivery Problem with respect to delivery time (DDT), introduced by Erlebach et al. [ISAAC 2022]. We first resolve an open question posed by Erlebach et al. [ISAAC 2022] by showing that even when the delivery network is a path graph, DDT admits no polynomial-time approximation within any polynomially encodable factor $a(n)$, unless P=NP. Additionally, we identify the intersection graph of the agents, where nodes represent agents and edges indicate an overlap of the movement areas of two agents, as an important structural concept. For path graphs, we show that DDT becomes tractable when parameterized by the treewidth $w$ of the intersection graph, and we present an exact FPT algorithm with running time $f(w)\cdot\text{poly}(n,k)$, for some computable function $f$. For general graphs, we give an FPT algorithm with running time $f(\Delta,w)\cdot\text{poly}(n,k)$, where $\Delta$ is the maximum degree of the intersection graph. In the special case where the intersection graph is a tree, we provide a simple polynomial-time algorithm.

Problem

• Drone Delivery Problem
• delivery time
• parameterized algorithms
• intersection graph
• logistics coordination

Innovation

• Drone Delivery Problem
• parameterized algorithms
• intersection graph
• treewidth
• fixed-parameter tractability