How to collect balls moving in the Euclidean plane

Yuichi Asahiro, Takashi Horiyama, Kazuhisa Makino, Hirotaka Ono, Toshinori Sakuma, Masafumi Yamashita

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)2247-2262
Number of pages16
JournalDiscrete Applied Mathematics
Volume154
Issue number16
DOIs
Publication statusPublished - Nov 1 2006

Fingerprint

Euclidean plane
Ball
Robots
Robot
Line
Moving Target
Tractability
Straight
Polynomial-time Algorithm
Polynomials

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Asahiro, Y., Horiyama, T., Makino, K., Ono, H., Sakuma, T., & Yamashita, M. (2006). How to collect balls moving in the Euclidean plane. 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.

In: Discrete Applied Mathematics, Vol. 154, No. 16, 01.11.2006, p. 2247-2262.

Research output: Contribution to journalArticle

Asahiro, Y, Horiyama, T, Makino, K, Ono, H, Sakuma, T & Yamashita, M 2006, 'How to collect balls moving in the Euclidean plane', Discrete Applied Mathematics, vol. 154, no. 16, pp. 2247-2262. https://doi.org/10.1016/j.dam.2006.04.020
Asahiro Y, Horiyama T, Makino K, Ono H, Sakuma T, Yamashita M. How to collect balls moving in the Euclidean plane. Discrete Applied Mathematics. 2006 Nov 1;154(16):2247-2262. https://doi.org/10.1016/j.dam.2006.04.020
Asahiro, Yuichi ; Horiyama, Takashi ; Makino, Kazuhisa ; Ono, Hirotaka ; Sakuma, Toshinori ; Yamashita, Masafumi. / How to collect balls moving in the Euclidean plane. In: Discrete Applied Mathematics. 2006 ; Vol. 154, No. 16. pp. 2247-2262.
@article{99a666b412004258abce2cf731b23dc4,
title = "How to collect balls moving in the Euclidean plane",
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.",
author = "Yuichi Asahiro and Takashi Horiyama and Kazuhisa Makino and Hirotaka Ono and Toshinori Sakuma and Masafumi Yamashita",
year = "2006",
month = "11",
day = "1",
doi = "10.1016/j.dam.2006.04.020",
language = "English",
volume = "154",
pages = "2247--2262",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",
number = "16",

}

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 -