Decomposition of integer matrices and multileaf collimator sequencing

DOI10.1016/j.dam.2005.04.008zbMath1084.15014OpenAlexW2084991719MaRDI QIDQ2576339

Davaatseren Baatar, Horst W. Hamacher, Matthias Ehrgott, Gerhard J. Woeginger

Publication date: 27 December 2005

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2005.04.008

zbMATH Keywords

algorithmsradiotherapyconsecutive ones propertydecomposition of integer matricesmultileaf collimator sequencingstop design in public transportation

Mathematics Subject Classification ID

Integer programming (90C10) Transportation, logistics and supply chain management (90B06) Biomedical imaging and signal processing (92C55) Positive matrices and their generalizations; cones of matrices (15B48) Matrices of integers (15B36)

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Cites Work

• Unnamed Item
• Unnamed Item
• Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms
• Inverse radiation therapy planning -- a multiple objective optimization approach
• THE CONTINUOUS STOP LOCATION PROBLEM IN PUBLIC TRANSPORTATION NETWORKS
• Minimizing beam-on time in cancer radiation treatment using multileaf collimators
• A network flow algorithm to minimize beam‐on time for unconstrained multileaf collimator problems in cancer radiation therapy