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 journalArticlepeer-review

3 Citations (Scopus)


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
Issue number16
Publication statusPublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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