### Abstract

An n-node tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NP-hard. We investigate the problem of distributed collective exploration of unknown trees. Not surprisingly, communication between robots influences the time of exploration. Our main communication scenario is the following: robots can communicate by writing at the currently visited node previously acquired information, and reading information available at this node. We construct an exploration algorithm whose running time for any tree is only O(k/ log k) larger than optimal exploration time with full knowledge of the tree. (We say that the algorithm has overhead O(k/ log k)). On the other hand we show that, in order to get overhead sublinear in the number of robots, some communication is necessary. Indeed, we prove that if robots cannot communicate at all, then every distributed exploration algorithm works in time Ω(k) larger than optimal exploration time with full knowledge, for some trees.

Original language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Martin Farach-Colton |

Publisher | Springer Verlag |

Pages | 141-151 |

Number of pages | 11 |

ISBN (Print) | 3540212582, 9783540212584 |

State | Published - Jan 1 2004 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 2976 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 141-151). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2976). Springer Verlag.

**Collective tree exploration.** / Fraigniaud, Pierre; Gasieniec, Leszek; Kowalski, Dariusz R.; Pelc, Andrzej.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2976, Springer Verlag, pp. 141-151.

}

TY - CHAP

T1 - Collective tree exploration

AU - Fraigniaud, Pierre

AU - Gasieniec, Leszek

AU - Kowalski, Dariusz R.

AU - Pelc, Andrzej

PY - 2004/1/1

Y1 - 2004/1/1

N2 - An n-node tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NP-hard. We investigate the problem of distributed collective exploration of unknown trees. Not surprisingly, communication between robots influences the time of exploration. Our main communication scenario is the following: robots can communicate by writing at the currently visited node previously acquired information, and reading information available at this node. We construct an exploration algorithm whose running time for any tree is only O(k/ log k) larger than optimal exploration time with full knowledge of the tree. (We say that the algorithm has overhead O(k/ log k)). On the other hand we show that, in order to get overhead sublinear in the number of robots, some communication is necessary. Indeed, we prove that if robots cannot communicate at all, then every distributed exploration algorithm works in time Ω(k) larger than optimal exploration time with full knowledge, for some trees.

AB - An n-node tree has to be explored by k mobile agents (robots), starting in its root. Every edge of the tree must be traversed by at least one robot, and exploration must be completed as fast as possible. Even when the tree is known in advance, scheduling optimal collective exploration turns out to be NP-hard. We investigate the problem of distributed collective exploration of unknown trees. Not surprisingly, communication between robots influences the time of exploration. Our main communication scenario is the following: robots can communicate by writing at the currently visited node previously acquired information, and reading information available at this node. We construct an exploration algorithm whose running time for any tree is only O(k/ log k) larger than optimal exploration time with full knowledge of the tree. (We say that the algorithm has overhead O(k/ log k)). On the other hand we show that, in order to get overhead sublinear in the number of robots, some communication is necessary. Indeed, we prove that if robots cannot communicate at all, then every distributed exploration algorithm works in time Ω(k) larger than optimal exploration time with full knowledge, for some trees.

UR - http://www.scopus.com/inward/record.url?scp=27644440909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27644440909&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:27644440909

SN - 3540212582

SN - 9783540212584

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 141

EP - 151

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Farach-Colton, Martin

PB - Springer Verlag

ER -