## Abstract

We introduce a new traversal technique in the context of piecemeal exploration of unknown graphs. The problem of learning a graph via piecemeal exploration requires a robot to create a complete map of its environment, subject to two constraints. First, it cannot jump between non-adjacent vertices in one time step and second, it must return to a fixed starting point every so often. This paper presents the recursive piecemeal search (RPS) strategy together with an algorithm for the above problem. We are able to achieve O(log^{2} n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(n^{ε}) overhead. The graph is discovered via the recursive piecemeal search, which can be viewed as a combination of breadth-first and depth-first passes. The construction of RPS trees relies on the concept of sparse neighborhood covers and captures nicely the nature of the graph exploration problem.

Original language | English (US) |
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Pages | 280-286 |

Number of pages | 7 |

State | Published - Jan 1 1998 |

Externally published | Yes |

Event | Proceedings of the 1998 11th Annual Conference on Computational Learning Theory - Madison, WI, USA Duration: Jul 24 1998 → Jul 26 1998 |

### Other

Other | Proceedings of the 1998 11th Annual Conference on Computational Learning Theory |
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City | Madison, WI, USA |

Period | 7/24/98 → 7/26/98 |

## ASJC Scopus subject areas

- Computational Mathematics