### Abstract

We consider the task of network exploration by a mobile agent (robot) with small memory. The agent has to traverse all nodes and edges of a network (represented as an undirected connected graph), and return to the starting node. Nodes of the network are unlabeled and edge ports are locally labeled at each node. The agent has no a priori knowledge of the topology of the network or of its size, and cannot mark nodes in any way. Under such weak assumptions, cycles in the network may prevent feasibility of exploration, hence we restrict attention to trees. We present an algorithm to accomplish tree exploration (with return) using O(log n)-bit memory for all n-node trees. This strengthens the result from Diks et al. [2004], where O(log^{2} n)-bit memory was used for tree exploration, and matches the lower bound on memory size proved there. We also extend our O(log n)-bit memory traversal mechanism to a weaker model in which ports at each node are ordered in circular manner, however, the explicit values of port numbers are not available.

Original language | English (US) |
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Article number | 17 |

Journal | ACM Transactions on Algorithms |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2011 |

Externally published | Yes |

### Keywords

- Distributed algorithms
- Graph exploration
- Small memory

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

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## Cite this

*ACM Transactions on Algorithms*,

*7*(2), [17]. https://doi.org/10.1145/1921659.1921663