Any Monotone Function Is Realized by Interlocked Polygons

Autor: Erik D. Demaine, Martin L. Demaine, Ryuhei Uehara
Jazyk: angličtina
Rok vydání: 2012
Předmět:
Zdroj: Algorithms, Vol 5, Iss 1, Pp 148-157 (2012)
Druh dokumentu: article
ISSN: 1999-4893
DOI: 10.3390/a5010148
Popis: 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.
Databáze: Directory of Open Access Journals