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Creators/Authors contains: "Demaine, Martin"

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  1. ; ; ; ; ; ; ; ; ; (, Thai Journal of Mathematics)
    Accepted Manuscript Full Text Available
  2. ; ; ; ; ; (, Computational Geometry)
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  3. ; ; ; (, Geombinatorics)
    Accepted Manuscript Full Text Available
  4. ; ; ; ; ; ; (, 24th Japan Conference on Discrete and Computational Geometry, Graphs, and Games)
    Accepted Manuscript Full Text Available
  5. ; ; ; ; ; ; ; ; (, Theoretical Computer Science)
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  6. ; ; ; ; ; ; ; ; ; (, The Electronic Journal of Combinatorics)
    null (Ed.)
    An open problem of Manuel Abellanas asks whether every set of disjoint closed unit disks in the plane can be connected by a conveyor belt, which means a tight simple closed curve that touches the boundary of each disk, possibly multiple times. We prove three main results: For unit disks whose centers are both $$x$$-monotone and $$y$$-monotone, or whose centers have $$x$$-coordinates that differ by at least two units, a conveyor belt always exists and can be found efficiently. It is NP-complete to determine whether disks of arbitrary radii have a conveyor belt, and it remains NP-complete when we constrain the belt to touch disks exactly once. Any disjoint set of $$n$$ disks of arbitrary radii can be augmented by $O(n)$ "guide" disks so that the augmented system has a conveyor belt touching each disk exactly once, answering a conjecture of Demaine, Demaine, and Palop. 
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