### Abstract

In this paper, we study how to collect n balls moving with constant velocities in the Euclidean plane by k robots moving on straight track-lines through the origin. Since all the balls might not be caught by robots, differently from Moving-Target TSP, we consider the following 3 problems in various situations: (i) deciding if k robots can collect all n balls, (ii) maximizing the number of the balls collected by k robots, and (iii) minimizing the number of the robots to collect all n balls. The situations considered here contain the cases in which track-lines are given (or not), and track-lines are identical (or not). For all problems and situations, we provide polynomial time algorithms or proofs of intractability, which clarify the tractability- intractability frontier in the ball collecting problems in the Euclidean plane.

Original language | English |
---|---|

Pages (from-to) | 229-245 |

Number of pages | 17 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 91 |

DOIs | |

Publication status | Published - Feb 16 2004 |

Event | Proceedings of Computing: The Australasian Theory Symposium (CATS) - Dunedin, New Zealand Duration: Jan 19 2004 → Jan 20 2004 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Electronic Notes in Theoretical Computer Science*,

*91*, 229-245. https://doi.org/10.1016/j.entcs.2003.12.015