Minimal Decomposition of a Digital Surface into Digital Plane Segments Is NP-Hard [chapter]

Isabelle Sivignon, David Coeurjolly
2006 Lecture Notes in Computer Science  
This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPS for short). We prove that the decision problem (does there exist a decomposition with less than k DPS?) is NP-complete, and thus that the optimisation problem (finding the minimal number of DPS) is NP-hard. The proof is based on a polynomial reduction of any instance of the well-known 3-SAT problem to an instance of the digital surface decomposition problem. A geometric model for the 3-SAT problem is proposed.
doi:10.1007/11907350_57 fatcat:fcgttwui7jdm7ltipx5fz6wy3u