Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
SIAM Journal on Control and Optimization
Minimax Rendezvous on the Line
SIAM Journal on Control and Optimization
Asymmetric rendezvous on the plane
Proceedings of the fourteenth annual symposium on Computational geometry
SIAM Journal on Control and Optimization
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Agent Rendezvous: A Dynamic Symmetry-Breaking Problem
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Gathering of Asynchronous Oblivious Robots with Limited Visibility
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Operations Research
Two Dimensional Rendezvous Search
Operations Research
Mobile Agent Rendezvous in a Ring
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Deterministic Rendezvous in Graphs
Algorithmica
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Undirected connectivity in log-space
Journal of the ACM (JACM)
Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements
SIAM Journal on Computing
Deterministic Rendezvous in Trees with Little Memory
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Randomized rendez-vous with limited memory
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Delays induce an exponential memory gap for rendezvous in trees
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
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
How to meet asynchronously (almost) everywhere
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Constructing a map of an anonymous graph: applications of universal sequences
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
DISC 2011 invited lecture: deterministic rendezvous in networks: survey of models and results
DISC'11 Proceedings of the 25th international conference on Distributed computing
How to meet in anonymous network
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
How to meet asynchronously at polynomial cost
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Deterministic polynomial approach in the plane
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Price of asynchrony in mobile agents computing
Theoretical Computer Science
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A team consisting of an unknown number of mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds. Each agent has a different label. Up to f of the agents are Byzantine. We consider two levels of Byzantine behavior. A strongly Byzantine agent can choose an arbitrary port when it moves and it can convey arbitrary information to other agents, while a weakly Byzantine agent can do the same, except changing its label. What is the minimum number of good agents that guarantees deterministic gathering of all of them, with termination? We solve exactly this Byzantine gathering problem in arbitrary networks for weakly Byzantine agents, and give approximate solutions for strongly Byzantine agents, both when the size of the network is known and when it is unknown. It turns out that both the strength versus weakness of Byzantine behavior and the knowledge of network size significantly impact the results. For weakly Byzantine agents we show that any number of good agents permit to solve the problem for networks of known size. If the size is unknown, then this minimum number is f + 2. More precisely, we show a deterministic polynomial algorithm that gathers all good agents in an arbitrary network, provided that there are at least f + 2 of them. We also provide a matching lower bound: we prove that if the number of good agents is at most f + 1, then they are not able to gather deterministically with termination in some networks. For strongly Byzantine agents we give a lower bound of f + 1, even when the graph is known: we show that f good agents cannot gather deterministically in the presence of f Byzantine agents even in a ring of known size. On the positive side we give deterministic gathering algorithms for at least 2f + 1 good agents when the size of the network is known, and for at least 4f + 2 good agents when it is unknown.