Introduction to algorithms
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
Agent Rendezvous: A Dynamic Symmetry-Breaking Problem
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A Space Lower Bound for Routing in Trees
STACS '02 Proceedings of the 19th 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
Universal Traversal Sequences with Backtracking
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Tree exploration with little memory
Journal of Algorithms
Asynchronous deterministic rendezvous in graphs
Theoretical Computer Science
Deterministic Rendezvous in Graphs
Algorithmica
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Deterministic rendezvous, treasure hunts and strongly universal exploration sequences
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Undirected connectivity in log-space
Journal of the ACM (JACM)
Randomized rendez-vous with limited memory
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
How to meet in anonymous network
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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 much memory is needed for leader election
DISC'10 Proceedings of the 24th international conference on Distributed computing
DISC 2011 invited lecture: deterministic rendezvous in networks: survey of models and results
DISC'11 Proceedings of the 25th international conference on Distributed computing
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Time vs. space trade-offs for rendezvous in trees
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Delays Induce an Exponential Memory Gap for Rendezvous in Trees
ACM Transactions on Algorithms (TALG)
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
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The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. The two identical agents start from arbitrary nodes in the graph and move from node to node with the goal of meeting. In this paper, we focus on rendezvous in trees, and, analogously to the efforts that have been made for solving the exploration problem with compact automata, we study the size of memory of mobile agents that permits to solve the rendezvous problem deterministically. We first show that if the delay between the starting times of the agents is arbitrary, then the lower bound on memory required for rendezvous is Ω(log n) bits, even for the line of length n. This lower bound meets a previously known upper bound of O(log n) bits for rendezvous in arbitrary trees of size at most n. Our main result is a proof that the amount of memory needed for rendezvous with simultaneous start depends essentially on the number L of leaves of the tree, and is exponentially less impacted by the number n of nodes. Indeed, we present two identical agents with O(log L + log log n) bits of memory that solve the rendezvous problem in all trees with at most n nodes and at most L leaves. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that Ω(log L + log log n) bits of memory is required for rendezvous, even in the class of trees with degrees bounded by 3.