Piecemeal graph exploration by a mobile robot (extended abstract)
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
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 Environments
SIAM Journal on Computing
Optimal constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
Tree exploration with little memory
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Networks
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
Rendezvous of Mobile Agents When Tokens Fail Anytime
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Mobile agent rendezvous in a ring using faulty tokens
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Tree exploration with logarithmic memory
ACM Transactions on Algorithms (TALG)
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 mobile agent has to explore an unknown network with unlabeled nodes: it must visit all nodes by walking along the links of the network, and eventually stop. If no upper bound on the size of the network is known and nodes of the network cannot be marked, then this exploration task cannot be accomplished for arbitrary networks by a deterministic terminating algorithm. On the other hand, it is feasible, if there is one unmovable token at the starting node of the agent. We investigate the exploration problem in arbitrary networks in the presence of identical unmovable tokens, some of which are Byzantine. A Byzantine token can be visible or invisible to the agent whenever the latter visits the node where the token is located, and visibility is decided by the adversary at each visit of the agent. If no upper bound on the number of tokens is known to the agent, deterministic exploration of all networks is impossible, even if all tokens are fault free. It is also impossible if all tokens are Byzantine, even if their number is known. Our main result is a deterministic exploration algorithm with cost polynomial in the (unknown) size of the network, which works in arbitrary networks, provided that the agent knows some upper bound on the total number of tokens, and that at least one token is fault free.