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
VL - 154
SP - 2247
EP - 2262
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 16
ER -