Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
An Experimental Study of a Cooperative Positioning System
Autonomous Robots
Proceedings of the 2004 joint workshop on Foundations of mobile computing
Localization and routing in sensor networks by local angle information
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Distributed localization using noisy distance and angle information
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Deterministic geoleader election in disoriented anonymous systems
Theoretical Computer Science
A distributed continuous-time algorithm for network localization using angle-of-arrival information
Automatica (Journal of IFAC)
Hi-index | 0.01 |
This paper provides a complexity study of the deterministic localization problem in robot networks using local and relative observations only. This is an important issue in collective and cooperative robotics where global positioning systems (GPS) are not available, and the basic premise is the localization ability of the group. We prove that given a set of relative observations made by the robots, the unique unambiguous pose estimation of the robot network in a deterministic way is an NP-hard problem. Thismeans that no polynomial-time algorithm can deterministically solve the unique pose estimation problem based on relative observations unless P = NP. The consequence is that no guarantee can be provided, in a polynomial time, that the possibly estimated poses of the robots will correspond to the effective (actual) ones. The proof is based on complexity theory where we build appropriate polynomial-time reductions interrelating the multirobot localization problem to a well-known NP-complete problem (the partition problem). This NP-hardness result opens questions and perspectives for research into approximations to overcome its intractability.