How to collect balls moving in the Euclidean plane

  • Authors:

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

  • Affiliations:

  • Department of Social Information Systems, Faculty of Information Science, Kyushu Sangyo University, Higashi-ku, Fukuoka, Japan;Department of Communications and Computer Engineering, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Mathematical Informatics, Graduate School of Information and Technology, University of Tokyo, Tokyo, Japan;Department of Computer Science and Communication Engineering, Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan;Toshiba Solutions Corporation, Minato-ku, Tokyo, Japan;Department of Computer Science and Communication Engineering, Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

  • Venue:
  • Discrete Applied Mathematics - Special issue: Discrete algorithms and optimization, in honor of professor Toshihide Ibaraki at his retirement from Kyoto University
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

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.