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

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.

• Type: Conference
• Year: 2006
• Where: DGCI
• Authors: Isabelle Sivignon, David Coeurjolly
• Keywords: 3-SAT Problem, DGCI 2006, Digital Surface, Discrete Geometry, Surface Decomposition Problem