Minimumdecompositionofadigitalsurfaceintodigitalplanesegments isNP-hard
DavidCoeurjolly IsabelleSivignon · 2009
a b s t r a c t Thispaperdealswiththecomplexityofthedecompositionofadigitalsurfaceintodigital plane segments (DPSs for short). We prove that the decision problem (does there exist a decomposition with less than DPSs?) is NP-complete, and thus that the optimization problem (finding the minimum number of DPSs) is NP-hard. The proof is based on a polynomialreductionofanyinstanceofthewell-known3-SATproblemtoaninstanceof the digital surface decomposition problem. A geometric model for the 3-SAT problem is proposed. ’2008ElsevierB.V.Allrightsreserved.