Constrained Decompositions of Integer Matrices and their Applications to Intensity Modulated Radiation Therapy

We consider combinatorial optimization problems arising in radiation therapy. Given a matrix I with non-negative integer entries, we seek for a decomposition of I as a weighted sum of binary matrices having the consecutive ones property, such that the total sum of the coefficients is minimized. The coefficients are restricted to be non-negative integers. Here, we investigate variants of the problem with additional constraints on the matrices used in the decomposition. Constraints appearing in the application include the interleaf motion and interleaf distance constraints. The former constraint was previously studied by Baatar et al. (Discrete Appl. Math., 2005) and Kalinowksi (Discrete Appl. Math., 2005). The latter constraint was independently considered by Kumar et al. (working paper, 2007) in the case where coefficients of the decomposition are not restricted to be integers. For both constraints, we prove that finding an optimal decomposition reduces to finding a maximum value pote...

• Type: Conference
• Year: 2008
• Where: COLOGNETWENTE
• Authors: Céline Engelbeen, Samuel Fiorini
• Keywords: COLOGNETWENTE 2008, Interleaf Distance Constraint, Interleaf Motion, Non-negative Integers, Optimization