Existence and hardness of conveyor belts
Name
9782-PDF file-33977-1-10-20201022.pdf
Description
Published version
Size
651.95 KB
Format
Adobe PDF
Checksum (MD5)
9276ec7bbf7f02902ec7483ca0bdb591
Author(s)
Demaine, Erik D
Demaine, Martin L
Date Issued
October 2020
Journal
Electronic Journal of Combinatorics
Publisher
The Electronic Journal of Combinatorics
Citation
Baird, Molly et al. “Existence and hardness of conveyor belts.” Electronic Journal of Combinatorics, 24, 7 (October 2020): P4.25 © 2020 The Author(s)
Version
Final published version
Abstract
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: 1. 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. 2. 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. 3. 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.37236/9782
