Distributed Algorithms for Unidirectional Networks
SIAM Journal on Computing
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Optimal constrained graph exploration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Interval routing schemes allow broadcasting with linear message-complexity
Distributed Computing
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Proceedings of the 4th GI-Conference on Theoretical Computer Science
Sense of direction in distributed computing
Theoretical Computer Science - Special issue: Distributed computing
Tree exploration with little memory
Journal of Algorithms
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Journal of Graph Theory
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Distributed exploration of an unknown graph
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Finding short right-hand-on-the-wall walks in graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
On the Power of Local Orientations
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Anonymous graph exploration without collision by mobile robots
Information Processing Letters
On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Fast periodic graph exploration with constant memory
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
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We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in a local manner (called local orientation) so that the automaton is able to distinguish them. Precisely, the edges incident to a node v are given port numbers from 1 to dv, where dv is the degree of v Periodic graph exploration means visiting every node infinitely often. We are interested in the length of the period, i.e., the maximum number of edge traversals between two consecutive visits of any node by the automaton in the same state and entering the node by the same port. This problem is unsolvable if local orientations are set arbitrarily. Given this impossibility result, we address the following problem: what is the mimimum function π(n) such that there exist an algorithm for setting the local orientation, and a finite automaton using it, such that the automaton explores all graphs of size n within the period π(n)? The best result so far is the upper bound π(n) ≤10n, by Dobrev et al. [SIROCCO 2005], using an automaton with no memory (i.e. only one state). In this paper we prove a better upper bound π(n) ≤4n. Our automaton uses three states but performs periodic exploration independently of its starting position and initial state