Agent Rendezvous: A Dynamic Symmetry-Breaking Problem
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
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STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
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Two Dimensional Rendezvous Search
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Mobile Agent Rendezvous in a Ring
ICDCS '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
Deterministic Rendezvous in Graphs
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Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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
A local O(n2) gathering algorithm
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
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Space-optimal rendezvous of mobile agents in asynchronous trees
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Time vs. space trade-offs for rendezvous in trees
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
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Two identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and move along its edges with the goal of meeting at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We study optimal time of completing this rendezvous task. For deterministic rendezvous we seek algorithms that achieve rendezvous whenever possible, while for randomized rendezvous we seek almost safe algorithms, which achieve rendezvous with probability at least 1−1/n in n-node trees, for sufficiently large n. We construct a deterministic algorithm that achieves rendezvous in time O(n) in n-node trees, whenever rendezvous is feasible, and we show that this time cannot be improved in general, even when agents start at distance 1 in bounded degree trees. We also show an almost safe algorithm that achieves rendezvous in time O(n) for arbitrary starting positions in any n-node tree. We then analyze when randomization can help to speed up rendezvous. For n-node trees of known constant maximum degree and for a known constant upper bound on the initial distance between the agents, we show an almost safe algorithm achieving rendezvous in time O(logn). By contrast, we show that for some trees, every almost safe algorithm must use time Ω(n), even for initial distance 1. This shows an exponential gap between randomized rendezvous time in trees of bounded degree and in arbitrary trees. Such a gap does not occur for deterministic rendezvous. All our upper bounds hold when agents start with an arbitrary delay, controlled by the adversary, and all our lower bounds hold even when agents start simultaneously.