### 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 [15], where O(log^{2} n)-bit memory was used for tree exploration, and matches the lower bound on memory size proved there.

Original language | English (US) |
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Title of host publication | Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 |

Publisher | Association for Computing Machinery |

Pages | 585-594 |

Number of pages | 10 |

ISBN (Electronic) | 9780898716245 |

State | Published - Jan 1 2007 |

Externally published | Yes |

Event | 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 - New Orleans, United States Duration: Jan 7 2007 → Jan 9 2007 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 07-09-January-2007 |

### Conference

Conference | 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007 |
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Country | United States |

City | New Orleans |

Period | 1/7/07 → 1/9/07 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007*(pp. 585-594). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 07-09-January-2007). Association for Computing Machinery.