{"id":"https://openalex.org/W1970469509","doi":"https://doi.org/10.1109/drcn.2007.4762272","title":"Integrally indecomposable polytopes and the survivable network design problem","display_name":"Integrally indecomposable polytopes and the survivable network design problem","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W1970469509","doi":"https://doi.org/10.1109/drcn.2007.4762272","mag":"1970469509"},"language":"en","primary_location":{"id":"doi:10.1109/drcn.2007.4762272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/drcn.2007.4762272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 6th International Workshop on Design and Reliable Communication Networks","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053088741","display_name":"Elke Eisenschmidt","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Elke Eisenschmidt","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091730054","display_name":"Matthias K\u00f6ppe","orcid":"https://orcid.org/0000-0003-2492-4139"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthias Koppe","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053088741"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0006,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73371648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9660999774932861,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.9219635725021362},{"id":"https://openalex.org/keywords/integrally-closed","display_name":"Integrally closed","score":0.6823834180831909},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6053748726844788},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5615907311439514},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4963725209236145},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.4833059310913086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4751336872577667},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4684135317802429},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44004952907562256},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4178631603717804},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.41685670614242554},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3810151219367981},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34172216057777405},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.279693603515625},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24004942178726196},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12225085496902466},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10530921816825867}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9219635725021362},{"id":"https://openalex.org/C205059728","wikidata":"https://www.wikidata.org/wiki/Q6042740","display_name":"Integrally closed","level":2,"score":0.6823834180831909},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6053748726844788},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5615907311439514},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4963725209236145},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.4833059310913086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4751336872577667},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4684135317802429},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44004952907562256},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4178631603717804},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.41685670614242554},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3810151219367981},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34172216057777405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.279693603515625},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24004942178726196},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12225085496902466},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10530921816825867},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/drcn.2007.4762272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/drcn.2007.4762272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 6th International Workshop on Design and Reliable Communication Networks","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1598700566","https://openalex.org/W1682076822","https://openalex.org/W1974706915","https://openalex.org/W1987493955","https://openalex.org/W2018214829","https://openalex.org/W2020130108","https://openalex.org/W2036991007","https://openalex.org/W2047900282","https://openalex.org/W2070016441","https://openalex.org/W2148613317","https://openalex.org/W2335197782"],"related_works":["https://openalex.org/W2383359835","https://openalex.org/W4301073953","https://openalex.org/W1959221251","https://openalex.org/W4300505904","https://openalex.org/W2950264496","https://openalex.org/W2964258226","https://openalex.org/W4389984179","https://openalex.org/W2012356705","https://openalex.org/W4366556206","https://openalex.org/W1896087765"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,25,37,47,51,58,62,84,88],"survivable":[3],"network":[4],"design":[5],"problem":[6,17],"for":[7],"fractional":[8],"flows":[9],"and":[10,13],"integral":[11],"capacities":[12],"demands.":[14],"While":[15],"this":[16],"was":[18],"modelled":[19],"using":[20],"so-called":[21],"metric":[22],"inequalities":[23],"in":[24],"past,":[26],"we":[27,74],"will":[28],"present":[29],"an":[30],"integer":[31],"program":[32],"which":[33],"is":[34,54],"based":[35],"on":[36],"automatic":[38],"linearization":[39],"of":[40,50,61,70,79,87],"non-linear":[41],"constraints.":[42],"It":[43],"turns":[44],"out":[45],"that":[46],"linear":[48,59],"relaxation":[49],"latter":[52],"formulation":[53],"actually":[55],"stronger":[56],"than":[57],"relaxations":[60],"previously":[63],"known":[64],"models.":[65],"Our":[66],"model":[67],"making":[68],"use":[69],"integrally":[71],"indecomposable":[72],"polytopes,":[73],"introduce":[75],"a":[76],"new":[77],"way":[78],"computing":[80],"these":[81],"polytopes":[82],"via":[83],"chamber":[85],"decomposition":[86],"parameter":[89],"space.":[90]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}