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:
This work was partially supported by the Scientific Grant-in-Aid by the Ministry of Education, Science, Sports and Culture of Japan. A preliminary version appeared in [2] .

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.

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U2 - 10.1016/j.dam.2006.04.020

DO - 10.1016/j.dam.2006.04.020

M3 - Article

AN - SCOPUS:33747841266

SN - 0166-218X

VL - 154

SP - 2247

EP - 2262

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 16

ER -