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 |
|---|---|
| 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 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Cite this
How to collect balls moving in the Euclidean plane. / Asahiro, Yuichi; Horiyama, Takashi; Makino, Kazuhisa; Ono, Hirotaka; Sakuma, Toshinori; Yamashita, Masafumi.
In: Discrete Applied Mathematics, Vol. 154, No. 16, 01.11.2006, p. 2247-2262.Research output: Contribution to journal › Article
}
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 -