How to decompose a binary matrix into three hv-convex polyominoes
Résumé
Given a binary matrix, deciding wether it can be decomposed into three hv-convex matrices is an NP-complete problem, whereas its decomposition into two hv-convex matrices or two hv-polyominoes can be performed in polynomial time. In this paper we give a polynomial time algorithm that decomposes a binary matrix into three hv-polyominoes, if such a decomposition exists. These problems are motivated by the Intensity Modulated Radiation Therapy (IMRT).