Near-Quadratic Inapproximability of Multi-Agent Pathfinding on Strongly Biconnected Digraphs
Year: 2026
Type: preprint
Abstract: This investigates the computational complexity and approximability of multi-agent pathfinding (MAPF) on directed graphs where feasible plans are guaranteed to exist. The paper establishes near-quadratic inapproximability for the minimum sequential move count and parallel final-arrival sum of costs, together with near-linear inapproximability for makespan, on always-feasible strongly biconnected digraphs with at least two unoccupied vertices, unless P = NP. The hardness results remain valid under multiple parallel-movement conventions governing following chains and occupied-cycle rotations, while head-on swaps are forbidden. The central reduction embeds a directed acyclic feasibility problem into a strongly biconnected network with occupied ballast structures. Escaping an infeasible core forces initially correctly placed agents to undertake long restoration walks, thereby generating the approximation gap without relying on infeasible output instances. On the constructive side, the paper derives an O(n²) approximation for sequential moves on feasible strongly biconnected instances, matching the hardness exponent. It also establishes a 7n² sum-of-costs approximation for a broad certified family of directed networks, using adaptive cycle selection and bounded-length agent–hole exchanges. Additional results address passing-bay algorithms, movement semantics and structural graph conditions. The work separates the complexity of finding feasible plans from the complexity of approximating optimal plans, while identifying the scope and limitations of the structural approximation guarantees. Deposited materials Main research manuscript (27 pages), including definitions, hardness theorems, approximation algorithms and mathematical appendices. Author: Shardul Mishra, School of Computer Science and Engineering (SCOPE), Vellore Institute of Technology, India. Copyright: © 2026 Shardul Mishra. All rights reserved.
Author: Mishra, Shardul
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224910702