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
Random walks on weighted graphs, and applications to on-line algorithms
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
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
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
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
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering asynchronous oblivious mobile robots in a ring
Theoretical Computer Science
How to meet in anonymous network
Theoretical Computer Science
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Asynchronous Deterministic Rendezvous on the Line
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring
Theoretical Computer Science
Tell me where i am so i can meet you sooner: asynchronous rendezvous with location information
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
Asynchronous deterministic rendezvous in graphs
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Linear time and space gathering of anonymous mobile agents in asynchronous trees
Theoretical Computer Science
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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Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent is continuous, does not leave its route and covers all of it. Meeting in a graph means that both agents must be at the same time in some node or in some point inside an edge of the graph, while meeting in a terrain means that both agents must be at the same time in some point of the terrain. Does there exist a deterministic algorithm that allows any two agents to meet in any unknown environment in spite of this very powerful adversary? We give deterministic rendezvous algorithms for agents starting at arbitrary nodes of any anonymous connected graph (finite or infinite) and for agents starting at any interior points with rational coordinates in any closed region of the plane with path-connected interior. In the geometric scenario agents may have different compasses and different units of length. While our algorithms work in a very general setting -- agents can, indeed, meet almost everywhere -- we show that none of these few limitations imposed on the environment can be removed. On the other hand, our algorithm also guarantees the following approximate rendezvous for agents starting at arbitrary interior points of a terrain as previously stated agents will eventually get to within an arbitrarily small positive distance from each other.