Minimum decomposition into convex binary matrices

Authors:
Fethi Jarray;Christophe Picouleau
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 6
Cited 1

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How to decompose a binary matrix into three hv-convex polyominoes

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Abstract

Motivated by Intensity Modulated Radiation Therapy, we consider the problem of the minimum decomposition of an integer matrix into hv-convex matrices with time and cardinality objectives. We study the special case where the matrix to decompose is a binary matrix (in this case, time decomposition and cardinality decomposition are the same). We prove that the decomposition into two hv-convex matrices or into two hv-convex polyominoes is polynomially solvable. For the decomposition into three hv-convex matrices the problem becomes NP-complete.