### Abstract

We introduce and study a new problem concerning the exploration of a geometric domain by mobile robots. Consider a line segment [0,I] and a set of n mobile robots r _{1},r _{2},⋯, r _{n} placed at one of its endpoints. Each robot has a searching speed s _{i} and a walking speed w _{i}, where s _{i} <w _{i} . We assume that every robot is aware of the number of robots of the collection and their corresponding speeds. At each time moment a robot r _{i} either walks along a portion of the segment not exceeding its walking speed w _{i}, or it searches a portion of the segment with speed not exceeding s _{i} . A search of segment [0,I] is completed at the time when each of its points have been searched by at least one of the n robots. We want to develop efficient mobility schedules (algorithms) for the robots which complete the search of the segment as fast as possible. More exactly we want to maximize the speed of the mobility schedule (equal to the ratio of the segment length versus the time of the completion of the schedule). We analyze first the offline scenario when the robots know the length of the segment that is to be searched. We give an algorithm producing a mobility schedule for arbitrary walking and searching speeds and prove its optimality. Then we propose an online algorithm, when the robots do not know in advance the actual length of the segment to be searched. The speed S of such algorithm is defined as where S(I _{L} ) denotes the speed of searching of segment I _{L} =[0,L]. We prove that the proposed online algorithm is 2-competitive. The competitive ratio is shown to be better in the case when the robots' walking speeds are all the same, approaching 1.29843 as n goes to infinity.

Original language | English (US) |
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Title of host publication | Structural Information and Communication Complexity - 21st International Colloquium, SIROCCO 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 23-36 |

Number of pages | 14 |

ISBN (Print) | 9783319096193 |

DOIs | |

State | Published - Jan 1 2014 |

Externally published | Yes |

Event | 21st International Colloquium on Structural Information and Communication Complexity, SIROCCO 2014 - Takayama, Japan Duration: Jul 23 2014 → Jul 25 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8576 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 21st International Colloquium on Structural Information and Communication Complexity, SIROCCO 2014 |
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Country | Japan |

City | Takayama |

Period | 7/23/14 → 7/25/14 |

### Keywords

- Algorithm
- Mobile Robots
- On-line
- Schedule
- Searching
- Segment
- Speed
- Walking

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Structural Information and Communication Complexity - 21st International Colloquium, SIROCCO 2014, Proceedings*(pp. 23-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8576 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-09620-9_4