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
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Operations Research
Two Dimensional Rendezvous Search
Operations Research
Rendezvous Search: A Personal Perspective
Operations Research
Geometrically aware communication in random wireless networks
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Collective tree spanners of graphs
SIAM Journal on Discrete Mathematics
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
How to meet in anonymous network
Theoretical Computer Science
On the effect of the deployment setting on broadcasting in Euclidean radio networks
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Using eventually consistent compasses to gather memory-less mobile robots with limited visibility
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
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
The Mobile Agent Rendezvous Problem in the Ring
The Mobile Agent Rendezvous Problem in the Ring
How to meet asynchronously (almost) everywhere
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Mobile agent rendezvous: a survey
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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We study rendezvous of two anonymous agents, where each agent knows its own initial position in the environment. Their task is to meet each other as quickly as possible. The time of the rendezvous is measured by the number of synchronous rounds that agents need to use in the worst case in order to meet. In each round, an agent may make a simple move or it may stay motionless. We consider two types of environments, finite or infinite graphs and Euclidean spaces. A simple move traverses a single edge (in a graph) or at most a unit distance (in Euclidean space). The rendezvous consists in visiting by both agents the same point of the environment simultaneously (in the same round). In this paper, we propose several asymptotically optimal rendezvous algorithms. In particular, we show that in the line and trees as well as in multidimensional Euclidean spaces and grids the agents can rendezvous in time O(d), where d is the distance between the initial positions of the agents. The problem of location-aware rendezvous was studied before in the asynchronous model for Euclidean spaces and multi-dimensional grids, where the emphasis was on the length of the adopted rendezvous trajectory. We point out that, contrary to the asynchronous case, where the cost of rendezvous is dominated by the size of potentially large neighborhoods, the agents are able to meet in all graphs of at most n nodes in time almost linear in d, namely, O(d log2 n). We also determine an infinite family of graphs in which synchronized rendezvous takes time Ω(d).