### Abstract

In this paper, we study how to collect n balls moving with a fixed constant velocity 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; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper 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 |
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Pages (from-to) | 2247-2262 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 154 |

Issue number | 16 |

DOIs | |

Publication status | Published - Nov 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*154*(16), 2247-2262. https://doi.org/10.1016/j.dam.2006.04.020

**How to collect balls moving in the Euclidean plane.** / Asahiro, Yuichi; Horiyama, Takashi; Makino, Kazuhisa; Ono, Hirotaka; Sakuma, Toshinori; Yamashita, Masafumi.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 154, no. 16, pp. 2247-2262. https://doi.org/10.1016/j.dam.2006.04.020

}

TY - JOUR

T1 - How to collect balls moving in the Euclidean plane

AU - Asahiro, Yuichi

AU - Horiyama, Takashi

AU - Makino, Kazuhisa

AU - Ono, Hirotaka

AU - Sakuma, Toshinori

AU - Yamashita, Masafumi

PY - 2006/11/1

Y1 - 2006/11/1

N2 - In this paper, we study how to collect n balls moving with a fixed constant velocity 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; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper 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.

AB - In this paper, we study how to collect n balls moving with a fixed constant velocity 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; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper 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.

UR - http://www.scopus.com/inward/record.url?scp=33747841266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747841266&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2006.04.020

DO - 10.1016/j.dam.2006.04.020

M3 - Article

AN - SCOPUS:33747841266

VL - 154

SP - 2247

EP - 2262

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 16

ER -