Minimum dominating sets of intervals on lines

Extended abstract
  • Siu-Wing Cheng
  • Michael Kaminski
  • Shmuel Zaks
Session 9B: Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


We study the problem of computing minimum dominating sets of n intervals on lines in three cases: (1) the lines intersect at a single point, (2) all lines except one are parallel, and (3) one line with t weighted points on it and the minimum dominating set must maximize the weight sum of the weighted points covered. We propose polynomial-time algorithms for the first two problems, which are special cases of the minimum dominating set problem for path graphs which is known to be NP-hard. The third problem requires identifying the structure of minimum dominating sets of intervals on a line so as to be able to select one that maximizes the weight sum of the weighted points covered. Assuming that presorting has been performed, the first problem has an O(n) time solution, while the second and the third problems are solved by dynamic programming algorithms, requiring O(n log n) and O(n+t) time, respectively.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Siu-Wing Cheng
    • 1
  • Michael Kaminski
    • 2
  • Shmuel Zaks
    • 2
  1. 1.Department of Computer ScienceHong Kong University of Science and TechnologyClear Water BayHong Kong
  2. 2.Department of Computer ScienceTechnion - Israel Institute of TechnologyHaifaIsrael

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