Optimal Path Planning in Hostile Environments

TL;DR

This paper introduces a new multi-agent path planning problem in hazardous environments with reactivating hazards, analyzing its computational complexity and providing algorithms for specific graph structures.

Contribution

It formalizes a novel multi-agent planning problem with hazards, proves NP-hardness, and offers polynomial solutions for certain graph classes.

Findings

Optimal plans require only polynomially many steps.

The problem is NP-hard on tree graphs.

Polynomial-time algorithm exists for path graphs.

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.