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
Optimal graph exploration without good maps
Theoretical Computer Science
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
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
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
Local spreading algorithms for autonomous robot systems
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
Arbitrary pattern formation by asynchronous, anonymous, oblivious robots
Theoretical Computer Science
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
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Network exploration by silent and oblivious robots
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Self-stabilizing tiny interaction protocols
Proceedings of the Third International Workshop on Reliability, Availability, and Security
How many oblivious robots can explore a line
Information Processing Letters
Review: Of robot ants and elephants: A computational comparison
Theoretical Computer Science
Robot networks with homonyms: the case of patterns formation
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Gathering of robots on anonymous grids without multiplicity detection
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
How to gather asynchronous oblivious robots on anonymous rings
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Optimal probabilistic ring exploration by semi-synchronous oblivious robots
Theoretical Computer Science
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In an 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 Asynch where 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, in general, exploration cannot be done efficiently. More precisely we prove that there are n-node trees where @W(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(lognloglogn) robots. The proof of the result is constructive. We also prove that the size of the team used in our solution is asymptotically optimal: there are trees of degree 3, whose exploration requires @W(lognloglogn) robots. Our final result shows that the difficulty in tree exploration comes in fact from the symmetries of the tree. Indeed, we show that, in order to explore trees that do not have any non-trivial automorphisms, 4 robots are always sufficient and often necessary.