Any Monotone Function Is Realized by Interlocked Polygons
Author(s)Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei
MetadataShow full item record
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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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.
Final published version