### Abstract

We address the problem of exploring an unknown graph G = (V, E) from a given start node s with either a tethered robot or a robot with a fuel tank of limited capacity, the former being a tighter constraint. In both variations of the problem, the robot can only move along the edges of the graph, i.e, it cannot jump between non-adjacent vertices. In the tethered robot case, if the tether (rope) has length /, then the robot must remain within distance / from the start node s. In the second variation, a fuel tank of limited capacity forces the robot to return to s after traversing C edges. The efficiency of algorithms for both variations of the problem is measured by the number of edges traversed during the exploration. We present an algorithm for a tethered robot which explores the graph in &Ogr;(|E|) edge traversais. The problem of exploration using a robot with a limited fuel tank capacity can be solved with a simple reduction from the tethered robot case and also yields a &Ogr;(|E|) algorithm. This improves on the previous best known bound of &Ogr;(|E| + \V|^{2}log ^{2}|V|) in [4]. Since the lower bound for the graph exploration problems is |E|, our algorithm is optimal, thus answering the open problem of Awerbuch, Betke, Rivest, and Singh [3].

Original language | English (US) |
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Title of host publication | Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms |

Publisher | Association for Computing Machinery (ACM) |

Pages | 807-814 |

Number of pages | 8 |

ISBN (Print) | 0898714907 |

State | Published - Jan 1 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
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Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

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### Keywords

- Algorithms
- Design
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 807-814). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery (ACM).