### 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) |
---|---|

Title of host publication | Proceedings of the Annual ACM Conference on Computational Learning Theory |

Publisher | ACM |

Pages | 280-286 |

Number of pages | 7 |

State | Published - 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 |
---|---|

City | Madison, WI, USA |

Period | 7/24/98 → 7/26/98 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mathematics

### Cite this

*Proceedings of the Annual ACM Conference on Computational Learning Theory*(pp. 280-286). ACM.

**Polylogarithmic-overhead piecemeal graph exploration.** / Awerbuch, Baruch; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM Conference on Computational Learning Theory.*ACM, pp. 280-286, Proceedings of the 1998 11th Annual Conference on Computational Learning Theory, Madison, WI, USA, 7/24/98.

}

TY - GEN

T1 - Polylogarithmic-overhead piecemeal graph exploration

AU - Awerbuch, Baruch

AU - Kobourov, Stephen G

PY - 1998

Y1 - 1998

N2 - 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(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) 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.

AB - 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(log2 n) overhead (where n is the number of vertices), improving on previous results of Awerbuch, Betke, Rivest, and Singh which require O(nε) 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.

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M3 - Conference contribution

SP - 280

EP - 286

BT - Proceedings of the Annual ACM Conference on Computational Learning Theory

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