2012/09/24 by Sarah R. Allen, Allen, Sarah R., John Iacono +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.1209.5307
arxiv created 2012/09/24 · arxiv updated 2012/09/25
Given a small polygon S, a big simple polygon B and a positive integer k, it is shown to be NP-hard to determine whether k copies of the small polygon (allowing translation and rotation) can be placed in the big polygon without overlap. Previous NP-hardness results were only known in the case where the big polygon is allowed to be non-simple. A novel reduction from Planar-Circuit-SAT is presented where a small polygon is constructed to encode the entire circuit.