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Any Monotone Function Is Realized by Interlocked Polygons
AbstractSuppose 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.
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Demaine, E.D.; Demaine, M.L.; Uehara, R. Any Monotone Function Is Realized by Interlocked Polygons. Algorithms 2012, 5, 148-157.View more citation formats
Demaine ED, Demaine ML, Uehara R. Any Monotone Function Is Realized by Interlocked Polygons. Algorithms. 2012; 5(1):148-157.Chicago/Turabian Style
Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei. 2012. "Any Monotone Function Is Realized by Interlocked Polygons." Algorithms 5, no. 1: 148-157.