Randomized algorithms
How to learn an unknown environment. I: the rectilinear case
Journal of the ACM (JACM)
Self-stabilization
Distributed Algorithms
The Polygon Exploration Problem
SIAM Journal on Computing
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Networks
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)
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
Local spreading algorithms for autonomous robot systems
Theoretical Computer Science
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Multiple Random Walks and Interacting Particle Systems
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The Mobile Agent Rendezvous Problem in the Ring
The Mobile Agent Rendezvous Problem in the Ring
Optimality and competitiveness of exploring polygons by mobile robots
Information and Computation
Network exploration by silent and oblivious robots
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Boundary patrolling by mobile agents with distinct maximal speeds
ESA'11 Proceedings of the 19th European conference on Algorithms
Position discovery for a system of bouncing robots
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Localization for a system of colliding robots
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We study a randomised distributed communication-less coordination mechanism for n uniform anonymous agents located on a circle with unit circumference. We assume the agents are located at arbitrary but distinct positions, unknown to other agents. The agents perform actions in synchronised rounds. At the start of each round an agent chooses the direction of its movement (clockwise or anticlockwise), and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction. Agents cannot leave marks on the ring, have zero vision and cannot exchange messages. However, on the conclusion of each round each agent has access to (some, not necessarily all) information regarding its trajectory during this round. This information can be processed and stored by the agent for further analysis. The location discovery task to be performed by each agent is to determine the initial position of every other agent and eventually to stop at its initial position, or proceed to another task, in a fully synchronised manner. Our primary motivation is to study distributed systems where agents collect the minimum amount of information that is necessary to accomplish this location discovery task. Our main result is a fully distributed randomised (Las Vegas type) algorithm, solving the location discovery problemw.h.p. in O(nlog2n) rounds (assuming the agents collect sufficient information). Note that our result also holds if initially the agents do not know the value of n and they have no coherent sense of direction.