Piecemeal Learning of an Unknown Environment
Machine Learning - Special issue on COLT '93
Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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 constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete 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
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Map construction of unknown graphs by multiple agents
Theoretical Computer Science
Journal of Graph Theory
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
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On the feasibility of gathering by autonomous mobile robots
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Remembering without Memory: Tree Exploration by Asynchronous Oblivious Robots
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Anonymous graph exploration without collision by mobile robots
Information Processing Letters
On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
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
Remembering without memory: Tree exploration by asynchronous oblivious robots
Theoretical Computer Science
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
Uniform multi-agent deployment on a ring
Theoretical Computer Science
Network exploration by silent and oblivious robots
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Optimal exploration of small rings
Proceedings of the Third International Workshop on Reliability, Availability, and Security
How many oblivious robots can explore a line
Information Processing Letters
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
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
On the self-stabilization of mobile oblivious robots in uniform rings
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security 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
Brief announcement: discovering and assessing fine-grained metrics in robot networks protocols
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
Optimal probabilistic ring exploration by semi-synchronous oblivious robots
Theoretical Computer Science
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We consider the problem of exploring an anonymous unoriented ring by a team of k identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimentional plane, but (with one exception) has not been investigated before. We indeed show that, although the lack of these capabilities renders the problems considerably more difficult, ring exploration is still possible. We show that the minimum number ρ(n) of robots that can explore a ring of size n is O(log n) and that ρ(n) = Ω(log n) for arbitrarily large n. On one hand we give an algorithm that explores the ring starting from any initial configuration, provided that n and k are co-prime, and we show that there always exist such k in O(log n). On the other hand we show that Ω(log n) agents are necessary for arbitrarily large n. Notice that, when k and n are not co-prime, the problem is sometimes unsolvable (i.e., there are initial configurations for which the exploration cannot be done). This is the case, e.g., when k divides n.