Any Monotone Function is Realized by Interlocked Polygons

• Demaine, Erik D.

• Demaine, Martin L.

• Uehara, Ryuhei

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 f 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.

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/10662

Journal

• Algorithms

  Algorithms 5 (1), 148-157, 2012-03-19

  MDPI Publishing

Keywords

• Computational Complexity
• interlocked polygons
• monotone Boolean function
• sliding block puzzle

Details

• CRID: 1050564287491765248
• NII Article ID: 120004288201
• ISSN: 19994893
• Web Site: http://hdl.handle.net/10119/10662
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles