Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Optimal graph exploration without good maps
Theoretical Computer Science
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Computing without communicating: ring exploration by asynchronous oblivious robots
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Gathering few fat mobile robots in the plane
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Local algorithms for autonomous robot systems
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Taking Advantage of Symmetries: Gathering of Asynchronous Oblivious Robots on a Ring
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring
Theoretical Computer Science
Exclusive perpetual ring exploration without chirality
DISC'10 Proceedings of the 24th international conference on Distributed computing
Optimal exploration of small rings
Proceedings of the Third International Workshop on Reliability, Availability, and Security
Optimal probabilistic ring exploration by semi-synchronous oblivious robots
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Optimal deterministic ring exploration with oblivious asynchronous robots
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Asynchronous exclusive perpetual grid exploration without sense of direction
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Optimal grid exploration by asynchronous oblivious robots
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
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In the effort to understand the algorithmic limitations of computing by a swarm of robots, the research has focused on the minimal capabilities that allow a problem to be solved. The weakest of the commonly used models is Asynchwhere the autonomous mobile robots, endowed with visibility sensors (but otherwise unable to communicate), operate in Look-Compute-Move cycles performed asynchronously for each robot. The robots are often assumed (or required to be) oblivious: they keep no memory of observations and computations made in previous cycles.We consider the setting when the robots are dispersed in an anonymous and unlabeled graph, and they must perform the very basic task of exploration: within finite time every node must be visited by at least one robot and the robots must enter a quiescent state. The complexity measure of a solution is the number of robots used to perform the task.We study the case when the graph is an arbitrary tree and establish some unexpected results. We first prove that there are n-node trees where 茂戮驴(n) robots are necessary; this holds even if the maximum degree is 4. On the other hand, we show that if the maximum degree is 3, it is possible to explore with only $O(\frac{\log n} {\log\log n})$ robots. The proof of the result is constructive. Finally, we prove that the size of the team is asymptotically optimal: we show that there are trees of degree 3 whose exploration requires $\Omega(\frac{\log n}{\log\log n})$ robots.