Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Networks
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
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
Undirected connectivity in log-space
Journal of the ACM (JACM)
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
How to meet when you forget: log-space rendezvous in arbitrary graphs
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Constructing a map of an anonymous graph: applications of universal sequences
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, possibly at different times, have to explore the network: every node must be visited by at least one agent and all agents must eventually stop. Agents are anonymous (identical), execute the same deterministic algorithm and move in synchronous rounds along links of the network. They are silent: they cannot send any messages to other agents or mark visited nodes in any way. In the absence of any additional information, exploration with termination of an arbitrary network in this weak model is impossible. Our aim is to solve the exploration problem giving to agents very restricted local traffic reports. Specifically, an agent that is at a node v in a given round, is provided with three bits of information, answering the following questions: Am I alone at v? Did any agent enter v in this round? Did any agent exit v in this round? We show that this small information permits to solve the exploration problem in arbitrary networks. More precisely, we give a deterministic terminating exploration algorithm working in arbitrary networks for all initial configurations that are not perfectly symmetric, i.e., in which there are agents with different views of the network. The algorithm works in time polynomial in the (unknown) size of the network. A deterministic terminating exploration algorithm working for all initial configurations in arbitrary networks does not exist.