mycoreobjectrosdok_document_0000028049rosdok_document_0000028049rosdokdocumentrosdok_derivate_00002299542026-10-23T10:27:33.385Z2026-10-23T10:18:52.575ZMCRJANITOReditorKEpublished1rosdok_derivate_0000229954truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok_id000059121987424867Oau2026-10-232026-10-23T10:22:30ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAnalgorithm for optimal multileaf collimator field segmentation with interleaf collision constraintIntensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of [5] so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.ThomasKalinowski1980 -VerfasserInaut1284202510000-0002-8444-6848https://purl.uni-rostock.de/rosdok/id00005912urn:nbn:de:gbv:28-rosdok_id00005912-810.18453/rosdok_id00005912510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (36 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005912Thomas Kalinowskirosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/20003-0002doctype:epubdoctype:epubDokumenttypDocument typedoctype:epub.workingpaperdoctype:epub.workingpaperWorkingpaperworking paperdiniPublType:workingPaper diniPublType2022:WorkingPaperinfo:eu-repo/semantics/workingPaperdocumentdiniPublType2022:WorkingPaperdiniPublType2022:WorkingPaperArbeitspapierWorking paperKDSF (Pu37)SDNB:510SDNB:510510 Mathematik510 Mathematicsinstitution:unirostockinstitution:unirostockUniversität RostockUniversity of RostockUniversität RostockUniversität RostockUni.Rostockhttp://d-nb.info/gnd/38329-6institution:unirostock.mnfinstitution:unirostock.mnfMathematisch-Naturwissenschaftliche FakultätFaculty of Mathematics and Natural SciencesUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätMathematisch-Natur-<br />wissenschaftliche FakultätUni.Rostock.Fakultaet.MNFhttp://d-nb.info/gnd/2147083-2licenseinfo:worklicenseinfo:workWerkworklicenseinfo:work.rightsreservedlicenseinfo:work.rightsreservedalle Rechte vorbehaltenall rights reserved/creativecommons/r/reserved/0.9/88x31.png[DE-28]Urheberrechtsschutz 1.0$gRights Statements$uhttp://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/http://rightsstatements.org/vocab/InC/1.0/licenseinfo:depositlicenseinfo:depositVeröffentlichungsgenehmigungpermission to storelicenseinfo:deposit.rightsunirostocklicenseinfo:deposit.rightsunirostockRechteinhaber Universität Rostockrightsholder Rostock Universityaccesscondition:openaccessaccesscondition:openaccessfrei zugänglich (Open Access)open accesshttp://purl.org/coar/access_right/c_abf2OAfreeinfo:eu-repo/semantics/openAccess[DE-28]Open Access$gControlled Vocabulary for Access Rights$uhttp://purl.org/coar/access_right/c_abf2licenseinfo:metadatalicenseinfo:metadataLizenzen für Metadatenlicenseinfo:metadata.cc0licenseinfo:metadata.cc0Lizenz Metadaten: CC0license metadata: CC0/creativecommons/p/zero/1.0/88x31.pnghttps://creativecommons.org/publicdomain/zero/1.0/rfc5646:enrfc5646:enEnglischEnglishengengAnalgorithm for optimal multileaf collimator field segmentation with interleaf collision constraintAn algorithm for optimal multileaf collimator field segmentation with interleaf collision constraintgnd:128420251orcid:0000-0002-8444-6848gnd:128420251orcid:0000-0002-8444-6848rosdok_document_0000028049-d3976508e50gnd:128420251orcid:0000-0002-8444-6848Thomas KalinowskiThomas KalinowskiThomas KalinowskiThomas KalinowskiThomas KalinowskiRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005912urn:nbn:de:gbv:28-rosdok_id00005912-810.18453/rosdok_id00005912Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of [5] so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/20003-0002https://purl.uni-rostock.de/rosdok/id000058163255797-8Thomas Kalinowskiepub.workingpaper1 Kalinowski_algorithm_2003.pdf 282326 11e575f6e41a5c79e4d081630af75ac0 rosdok_id000059121987424867Oau2026-10-232026-10-23T10:22:30ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAnalgorithm for optimal multileaf collimator field segmentation with interleaf collision constraintIntensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of [5] so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.ThomasKalinowski1980 -VerfasserInaut1284202510000-0002-8444-6848https://purl.uni-rostock.de/rosdok/id00005912urn:nbn:de:gbv:28-rosdok_id00005912-810.18453/rosdok_id00005912510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (36 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005912Thomas Kalinowskirosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/20003-0002 2026-10-23T10:18:52.575Z 2026-10-23T10:27:33.385Z 2026-11-02T10:27:33.416Z editorKE {"identifier":"rosdok/id00005912","type":"local_id","additional":"","service":"MCRLocalID","created":"2026-10-23T10:18:52.587Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00005912-8","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2026-10-23T10:18:52.600Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00005912","type":"purl","additional":"","service":"RosDokPURL","created":"2026-10-23T10:18:52.604Z","registrationStarted":"2026-10-23T10:27:32.245Z"} {"identifier":"10.18453/rosdok_id00005912","type":"doi","additional":"","service":"RosDokDOI","created":"2026-10-23T10:18:52.608Z","registrationStarted":"2026-10-23T10:27:31.930Z","registered":"2026-10-23T10:27:33.384Z"} MCRJANITORfulltextfile/rosdok_document_0000028049/rosdok_derivate_0000229954/Kalinowski_algorithm_2003.pdfAnalgorithm for optimal multileaf collimator field segmentation with interleaf collision constraintAn algorithm for optimal multileaf collimator field segmentation with interleaf collision constraintgnd:128420251orcid:0000-0002-8444-6848gnd:128420251orcid:0000-0002-8444-6848rosdok_document_0000028049-d3976508e50gnd:128420251orcid:0000-0002-8444-6848Thomas KalinowskiThomas KalinowskiThomas KalinowskiThomas KalinowskiThomas KalinowskiRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005912urn:nbn:de:gbv:28-rosdok_id00005912-810.18453/rosdok_id00005912Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of [5] so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient algorithm that constructs a segmentation with this minimal number of monitor units.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/20003-0002https://purl.uni-rostock.de/rosdok/id000058163255797-8Thomas Kalinowski[xslt]Saxonrosdok_id00005912https://purl.uni-rostock.de/rosdok/id00005912198742486710.18453/rosdok_id00005912urn:nbn:de:gbv:28-rosdok_id00005912-8Thomas KalinowskiKalinowski ThomasAn algorithm for optimal multileaf collimator field segmentation with interleaf collision constraintWorkingpaperworking paperUniversity of Rostock, Institute of Mathematics, 2003Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions…rosdok_id000058160003-000203/2Thomas KalinowskiAnalgorithm for optimal multileaf collimator field segmentation with interleaf collision constraintPreprints aus dem Institut für MathematikUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005912ThomasKalinowski1980 -VerfasserInaut1284202510000-0002-8444-6848[purl]https://purl.uni-rostock.de/rosdok/id00005912[urn]urn:nbn:de:gbv:28-rosdok_id00005912-8[doi]10.18453/rosdok_id00005912open_access20032003epoch:21th_centuryrfc5646:endoctype:epub.workingpaperaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published