Optimal Path Planning in Hostile Environments

2026-03-19

AI Summary

This study addresses a novel multi-agent path planning problem in which multiple agents originate from a common source and must cooperatively navigate toward a shared destination through a graph containing periodically cooling hazardous nodes; any agent contacting such a node is eliminated. The objective is to maximize the number of agents that successfully reach the goal. Within a deterministic, fully observable discrete-time setting, the problem is formally defined for the first time. The authors establish that the length of an optimal solution is polynomially bounded and prove that the problem remains NP-hard even when restricted to tree-structured graphs. However, they also identify a tractable case: when the underlying graph consists of vertex-disjoint paths, the problem admits a polynomial-time algorithm. Through rigorous complexity analysis and graph-theoretic modeling, this work delineates the computational boundaries of the problem.

Technology Category

• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Intelligent Robots: Motion and Path Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Tracking, profiling, and countermeasures against them

Abstract

Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze the computational complexity of a new multi-agent path planning problem that captures this setting. A group of identical agents begins at a common start location and must navigate a graph-based environment to reach a common target. The graph contains hazards that eliminate agents upon contact but then enter a known cooldown period before reactivating. In this discrete-time, fully-observable, deterministic setting, the planning task is to compute a movement schedule that maximizes the number of agents reaching the target. We first prove that, despite the exponentially large space of feasible plans, optimal plans require only polynomially-many steps, establishing membership in NP. We then show that the problem is NP-hard even when the environment graph is a tree. On the positive side, we present a polynomial-time algorithm for graphs consisting of vertex-disjoint paths from start to target. Our results establish a rich computational landscape for this problem, identifying both intractable and tractable fragments.

Problem

• multi-agent path planning
• hostile environments
• computational complexity
• hazardous graph traversal
• NP-hardness

Innovation

• multi-agent path planning
• hazardous environments
• computational complexity
• NP-hardness
• polynomial-time algorithm