Distributed Algorithms for Unidirectional Networks
SIAM Journal on Computing
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
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
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
Almost optimal asynchronous rendezvous in infinite multidimensional grids
DISC'10 Proceedings of the 24th international conference on Distributed computing
More efficient periodic traversal in anonymous undirected graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
More efficient periodic traversal in anonymous undirected graphs
Theoretical Computer Science
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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 d"v, where d"v 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 minimum function @p(n) such that there exists 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 @p(n)? The best result so far is the upper bound @p(n)@?10n, by Dobrev et al. [S. Dobrev, J. Jansson, K. Sadakane, W.-K. Sung, Finding short right-hand-on-the-wall walks in graphs, in: 12th Colloquium on Structural Information and Communication Complexity, SIROCCO, in: LNCS, vol. 3499, 2005, pp. 127-139], using an automaton with no memory (i.e. only one state). In this paper we prove a better upper bound @p(n)@?4n. Our automaton uses three states but performs periodic exploration independently of its starting position and initial state.