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 journalConference article

7 Citations (Scopus)

Abstract

In this paper, we study how to collect n balls moving with constant velocities 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, and (iii) minimizing the number of the robots to collect all n balls. The situations considered here 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)229-245
Number of pages17
JournalElectronic Notes in Theoretical Computer Science
Volume91
DOIs
Publication statusPublished - Feb 16 2004
EventProceedings of Computing: The Australasian Theory Symposium (CATS) - Dunedin, New Zealand
Duration: Jan 19 2004Jan 20 2004

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Asahiro, Y., Horiyama, T., Makino, K., Ono, H., Sakuma, T., & Yamashita, M. (2004). How to collect balls moving in the euclidean plane. Electronic Notes in Theoretical Computer Science, 91, 229-245. https://doi.org/10.1016/j.entcs.2003.12.015