Problems complete for deterministic logarithmic space
Journal of Algorithms
A random polynomial time algorithm for approximating the volume of convex bodies
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Rendezvous Search on the Line With Distinguishable Players
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Rendezvous Search on the Line with Indistinguishable Players
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
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Polynomial deterministic rendezvous in arbitrary graphs
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
How to meet in anonymous network
Theoretical Computer Science
Randomized rendez-vous with limited memory
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Uniform multi-agent deployment on a ring
Theoretical Computer Science
Randomized rendezvous with limited memory
ACM Transactions on Algorithms (TALG)
Mobile agent rendezvous: a survey
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
How to meet in anonymous network
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Gathering asynchronous oblivious mobile robots in a ring
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Black hole search in directed graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Periodic data retrieval problem in rings containing a malicious host
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
How to meet asynchronously (almost) everywhere
ACM Transactions on Algorithms (TALG)
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Two mobile agents (robots) having distinct labels and located in nodes of an unknown anonymous connected graph, have to meet. We consider the asynchronous version of this well-studied rendezvous problem and we seek fast deterministic algorithms for it. Since in the asynchronous setting meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well. The measure of performance of a rendezvous algorithm is its cost: for a given initial location of agents in a graph, this is the number of edge traversals of both agents until rendezvous is achieved. If agents are initially situated at a distance D in an infinite line, we show a rendezvous algorithm with cost O(D|Lmin|2) when D is known and O((D + |Lmax|)3) if D is unknown, where |Lmin| and |Lmax| are the lengths of the shorter and longer label of the agents, respectively. These results still hold for the case of the ring of unknown size but then we also give an optimal algorithm of cost O(n|Lmin|), if the size n of the ring is known, and of cost O(n|Lmax|), if it is unknown. For arbitrary graphs, we show that rendezvous is feasible if an upper bound on the size of the graph is known and we give an optimal algorithm of cost O(D|Lmin|) if the topology of the graph and the initial positions are known to agents.