{"id":"https://openalex.org/W2157810040","doi":"https://doi.org/10.1007/s11590-014-0773-3","title":"Complexity of the robust weighted independent set problems on interval graphs","display_name":"Complexity of the robust weighted independent set problems on interval graphs","publication_year":2014,"publication_date":"2014-08-02","ids":{"openalex":"https://openalex.org/W2157810040","doi":"https://doi.org/10.1007/s11590-014-0773-3","mag":"2157810040"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-014-0773-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-014-0773-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-014-0773-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11590-014-0773-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082213199","display_name":"Adam Kasperski","orcid":"https://orcid.org/0000-0003-1956-1812"},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Adam Kasperski","raw_affiliation_strings":["Institute of Industrial Engineering and Management, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370\u00a0, Wroc\u0142aw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Industrial Engineering and Management, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370\u00a0, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035521253","display_name":"Pawe\u0142 Zieli\u0144ski","orcid":"https://orcid.org/0000-0002-1466-2887"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Zieli\u0144ski","raw_affiliation_strings":["Institute of Mathematics and Computer Science, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370\u00a0, Wroc\u0142aw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, Wroc\u0142aw University of Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370\u00a0, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082213199"],"corresponding_institution_ids":["https://openalex.org/I11923345"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4204,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72176434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"3","first_page":"427","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10969","display_name":"Water resources management and optimization","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.8460766077041626},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6514464616775513},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.624915599822998},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.597919762134552},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5431740283966064},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.522777259349823},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4864940047264099},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46801483631134033},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4678294062614441},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42570292949676514},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.24487125873565674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22251546382904053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19820690155029297},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08454188704490662}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.8460766077041626},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6514464616775513},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.624915599822998},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.597919762134552},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5431740283966064},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.522777259349823},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4864940047264099},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46801483631134033},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4678294062614441},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42570292949676514},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.24487125873565674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22251546382904053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19820690155029297},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08454188704490662},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11590-014-0773-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-014-0773-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-014-0773-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11590-014-0773-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-014-0773-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-014-0773-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G836749445","display_name":null,"funder_award_id":"2013/09/B/ST6/01525","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2157810040.pdf","grobid_xml":"https://content.openalex.org/works/W2157810040.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W204341840","https://openalex.org/W347205678","https://openalex.org/W1963888335","https://openalex.org/W1992051595","https://openalex.org/W2007863759","https://openalex.org/W2011039300","https://openalex.org/W2026900294","https://openalex.org/W2032232293","https://openalex.org/W2051407192","https://openalex.org/W2111523610","https://openalex.org/W4253347690","https://openalex.org/W4285719527","https://openalex.org/W6631722374"],"related_works":["https://openalex.org/W2971351794","https://openalex.org/W4376155396","https://openalex.org/W1947085858","https://openalex.org/W2101991911","https://openalex.org/W2174986909","https://openalex.org/W2527791220","https://openalex.org/W2398738602","https://openalex.org/W2965171438","https://openalex.org/W1589381382","https://openalex.org/W961142965"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,20],"the":[4,11,52,60,71,79,85,95,104,107,111,119,142,152,160],"max\u2013min":[5,108],"and":[6,33,48,67,130,166],"min\u2013max":[7,123,161],"regret":[8,124,162],"versions":[9],"of":[10,54,59,97,103,110],"maximum":[12],"weighted":[13],"independent":[14],"set":[15],"problem":[16,112],"on":[17],"interval":[18,153],"graphs":[19],"uncertain":[21],"vertex":[22],"weights.":[23],"Both":[24],"problems":[25,72,143],"have":[26,146],"been":[27],"recently":[28],"investigated":[29],"by":[30],"Talla":[31],"Nobibon":[32],"Leus":[34],"(Optim":[35],"Lett":[36],"8:227\u2013235,":[37],"2014),":[38],"who":[39],"showed":[40],"that":[41,93,159],"they":[42],"are":[43,75],"NP-hard":[44,50,165],"for":[45,70,84,137,151],"two":[46],"scenarios":[47,55,98],"strongly":[49],"if":[51,94],"number":[53,96],"is":[56,91,100,113,126,157,164],"a":[57,101],"part":[58,102],"input.":[61],"In":[62],"this":[63],"paper,":[64],"new":[65],"complexity":[66],"approximation":[68],"results":[69],"under":[73],"consideration":[74],"provided,":[76],"which":[77],"extend":[78],"ones":[80],"previously":[81],"obtained.":[82],"Namely,":[83],"discrete":[86],"scenario":[87],"uncertainty":[88,154],"representation":[89,155],"it":[90,156],"proven":[92],"$$K$$":[99,129],"input,":[105],"then":[106],"version":[109,125,163],"not":[114,131],"at":[115],"all":[116],"approximable.":[117],"On":[118],"other":[120],"hand,":[121],"its":[122],"approximable":[127,132,167],"within":[128,133,168],"$$O(\\log":[134],"^{1-\\epsilon":[135],"}K)$$":[136],"any":[138],"$$\\epsilon":[139],">0$$":[140],"unless":[141],"in":[144],"NP":[145],"quasi":[147],"polynomial":[148],"algorithms.":[149],"Furthermore,":[150],"shown":[158],"2.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}