Any Monotone Function Is Realized by Interlocked Polygons
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Demaine_Any monotone.pdf
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2.14 MB
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Adobe PDF
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Uehara, Ryuhei
Date Issued
March 2012
Journal
Algorithms
Publisher
MDPI AG
Citation
Demaine, Erik D., Martin L. Demaine, and Ryuhei Uehara. “Any Monotone Function Is Realized by Interlocked Polygons.” Algorithms 5, no. 4 (March 19, 2012): 148–157.
Version
Final published version
Abstract
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets that makes the set of interlocked polygons free (not interlocked). This abstracts the essence of a kind of sliding block puzzle. We show that any monotone Boolean function ƒ on n variables can be described by m = O(n) interlocked polygons. We also show that the decision problem that asks if given polygons are interlocked is PSPACE-complete.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.3390/a5010148
