Any Monotone Function Is Realized by Interlocked Polygons
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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.
Date issued
2012-03Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
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
ISSN
1999-4893