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

N1 - Funding Information:
The authors would like to thank Prof. Tiko Kameda and Prof. Ichiro Suzuki for their helpful comments. This work was partially supported by the Scientific Grant-in-Aid by the Ministry of Education, Science, Sports and Culture of Japan.

PY - 2004/2/16

Y1 - 2004/2/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=18944362266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18944362266&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2003.12.015

DO - 10.1016/j.entcs.2003.12.015

M3 - Conference article

AN - SCOPUS:18944362266

VL - 91

SP - 229

EP - 245

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

T2 - Proceedings of Computing: The Australasian Theory Symposium (CATS)

Y2 - 19 January 2004 through 20 January 2004

ER -