Minimum decomposition of a digital surface into digital plane segments is NP-hard

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• 作者：Isabelle Sivignon ; David Coeurjolly
• 关键词：Digital object ; Digital plane ; Decomposition ; Complexity
• 刊名：Discrete Applied Mathematics
• 出版年：2009
• 出版时间：6 February 2009
• 年：2009
• 卷：157
• 期：3
• 页码：558-570
• 全文大小：3442 K

文摘

This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPSs for short). We prove that the decision problem (does there exist a decomposition with less than λ 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 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.