A public key cryptosystem based on Lyndon words
Information Processing Letters
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Distributed Algorithms
Circle formation for oblivious anonymous mobile robots with no common sense of orientation
Proceedings of the second ACM international workshop on Principles of mobile computing
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Periodic musical sequences and Lyndon words
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Coordination without communication: the case of the flocking problem
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
STAR: an algorithm to Search for Tandem Approximate Repeats
Bioinformatics
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing)
Circle formation of weak robots and Lyndon words
Information Processing Letters
Local spreading algorithms for autonomous robot systems
Theoretical Computer Science
Arbitrary pattern formation by asynchronous, anonymous, oblivious robots
Theoretical Computer Science
Circle formation of weak mobile robots
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
A Self-stabilizing Marching Algorithm for a Group of Oblivious Robots
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Deterministic leader election in anonymous sensor networks without common coordinated system
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Stabilizing flocking via leader election in robot networks
SSS'07 Proceedings of the 9h international conference on Stabilization, safety, and security of distributed systems
Deterministic robot-network localization is hard
IEEE Transactions on Robotics
Leader election problem versus pattern formation problem
DISC'10 Proceedings of the 24th international conference on Distributed computing
Biangular circle formation by asynchronous mobile robots
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Distributed Computing by Oblivious Mobile Robots
Distributed Computing by Oblivious Mobile Robots
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Consider a network made of n nodes scattered in the 2-dimensional space. Nodes are anonymous and disoriented devices being unable to communicate. Anonymous refers to systems made of a priori indistinguishable nodes. By disoriented, we mean that the nodes share no kind of coordinate system nor common sense of direction. Such systems are typically wireless sensor networks or swarms of robots endowed with localization capabilities, for instance visibility sensors or pattern formation maps. We address the Geoleader Election (GE) problem which is to ensure that, solely based on their positions, the nodes deterministically agree on the same position of a single node, called the leader. We provide a complete characterization on the node positions, both for systems with common handedness (chirality) and for systems devoid of a common handedness. The characterization is based on a particular object from combinatorics on words, namely the Lyndon words.