mycoreobjectrosdok_document_0000028045rosdok_document_0000028045rosdokdocumentrosdok_derivate_00002299462026-10-23T08:46:58.888Z2026-10-22T16:43:11.242ZeditorKEeditorKEpublished1rosdok_derivate_0000229946truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok_id000059091987393066Oau2026-10-222026-10-23T08:46:57ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAnew algorithm for optimal multileaf collimator field segmentationWe present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units and the number of segments. We will present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides in addition a solution with a very small number of segments.KonradEngel1956 -VerfasserInaut138612366https://purl.uni-rostock.de/rosdok/id00005909urn:nbn:de:gbv:28-rosdok_id00005909-610.18453/rosdok_id00005909510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (17 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005909Konrad Engelrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/50003-0005doctype: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:enEnglischEnglishengengAnew algorithm for optimal multileaf collimator field segmentationA new algorithm for optimal multileaf collimator field segmentationgnd:138612366gnd:138612366rosdok_document_0000028045-d3975716e50gnd:138612366Konrad EngelKonrad EngelKonrad EngelKonrad EngelKonrad EngelRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005909urn:nbn:de:gbv:28-rosdok_id00005909-610.18453/rosdok_id00005909We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units and the number of segments. We will present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides in addition a solution with a very small number of segments.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/50003-0005https://purl.uni-rostock.de/rosdok/id000058163255797-8Konrad Engelepub.workingpaper1 Engel_algorithm_2003.pdf 154531 7d30031e42d87350854f894b4e94d205 rosdok_id000059091987393066Oau2026-10-222026-10-23T08:46:57ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.14-SNAPSHOT [SCM: "" "" ""] with mode 'DEFAULT'.WorkingpaperAnew algorithm for optimal multileaf collimator field segmentationWe present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units and the number of segments. We will present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides in addition a solution with a very small number of segments.KonradEngel1956 -VerfasserInaut138612366https://purl.uni-rostock.de/rosdok/id00005909urn:nbn:de:gbv:28-rosdok_id00005909-610.18453/rosdok_id00005909510 MathematikMathematisch-Naturwissenschaftliche Fakultätalle Rechte vorbehaltenRechteinhaber Universität Rostockfrei zugänglich (Open Access)Lizenz Metadaten: CC0en1 Online-Ressource (17 Seiten)2003University of Rostock, Institute of MathematicsRostockmonographic20032026Universitätsbibliothek RostockRostock2026Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005909Konrad Engelrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/50003-0005 2026-10-22T16:43:11.242Z 2026-10-23T08:46:58.888Z 2026-11-02T08:46:58.921Z editorKE {"identifier":"rosdok/id00005909","type":"local_id","additional":"","service":"MCRLocalID","created":"2026-10-22T16:43:11.265Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00005909-6","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2026-10-22T16:43:11.277Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00005909","type":"purl","additional":"","service":"RosDokPURL","created":"2026-10-22T16:43:11.283Z","registrationStarted":"2026-10-23T08:03:38.696Z"} {"identifier":"10.18453/rosdok_id00005909","type":"doi","additional":"","service":"RosDokDOI","created":"2026-10-22T16:43:11.288Z","registrationStarted":"2026-10-23T08:03:38.387Z","registered":"2026-10-23T08:03:39.917Z"} editorKEfulltextfile/rosdok_document_0000028045/rosdok_derivate_0000229946/Engel_algorithm_2003.pdfAnew algorithm for optimal multileaf collimator field segmentationA new algorithm for optimal multileaf collimator field segmentationgnd:138612366gnd:138612366rosdok_document_0000028045-d3975716e50gnd:138612366Konrad EngelKonrad EngelKonrad EngelKonrad EngelKonrad EngelRostockUniversity of Rostock, Institute of Mathematicsepub.workingpaperhttps://purl.uni-rostock.de/rosdok/id00005909urn:nbn:de:gbv:28-rosdok_id00005909-610.18453/rosdok_id00005909We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units and the number of segments. We will present a short exact proof for a formula giving the smallest total number of monitor units and describe a class of algorithms yielding this minimal value. A special member of this class provides in addition a solution with a very small number of segments.20032003Preprints aus dem Institut für Mathematikrosdok_id000058161986139832Odvhttps://purl.uni-rostock.de/rosdok/id00005816Preprints aus dem Institut für Mathematik3255797-803/50003-0005https://purl.uni-rostock.de/rosdok/id000058163255797-8Konrad Engel[xslt]Saxonrosdok_id00005909https://purl.uni-rostock.de/rosdok/id00005909198739306610.18453/rosdok_id00005909urn:nbn:de:gbv:28-rosdok_id00005909-6Konrad EngelEngel KonradA new algorithm for optimal multileaf collimator field segmentationWorkingpaperworking paperUniversity of Rostock, Institute of Mathematics, 2003We present a new efficient leaf sequencing algorithm for the generation of intensity maps by a nonnegative combination of segments. Intensity maps describe the intensity modulation of beams in radiotherapy. We only study the static case (stop and shoot) an optimize the total number of monitor units…rosdok_id000058160003-000503/5Konrad EngelAnew algorithm for optimal multileaf collimator field segmentationPreprints aus dem Institut für MathematikUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00005909KonradEngel1956 -VerfasserInaut138612366[purl]https://purl.uni-rostock.de/rosdok/id00005909[urn]urn:nbn:de:gbv:28-rosdok_id00005909-6[doi]10.18453/rosdok_id00005909open_access20032003epoch:21th_centuryrfc5646:endoctype:epub.workingpaperaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published