{"id":"https://openalex.org/W7162763756","doi":"https://doi.org/10.48550/arxiv.2605.30053","title":"A Radius-Sensitive Approximation Algorithm for Connected Submodular Maximization","display_name":"A Radius-Sensitive Approximation Algorithm for Connected Submodular Maximization","publication_year":2026,"publication_date":"2026-05-28","ids":{"openalex":"https://openalex.org/W7162763756","doi":"https://doi.org/10.48550/arxiv.2605.30053"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.30053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30053","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.30053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093338782","display_name":"Philip Cervenjak","orcid":"https://orcid.org/0000-0002-8349-619X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cervenjak, Philip","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068471095","display_name":"Junhao Gan","orcid":"https://orcid.org/0000-0001-9101-1503"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gan, Junhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047111221","display_name":"Naonori Kakimura","orcid":"https://orcid.org/0000-0002-3918-3479"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kakimura, Naonori","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137395656","display_name":"Seeun William Umboh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Umboh, Seeun William","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136873369","display_name":"Anthony Wirth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wirth, Anthony","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8560000061988831,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8560000061988831,"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"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.04560000076889992,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.012600000016391277,"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/submodular-set-function","display_name":"Submodular set function","score":0.7989000082015991},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.7204999923706055},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5931000113487244},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5065000057220459},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.4740999937057495},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.4348999857902527},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.4250999987125397},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.3982999920845032},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.38679999113082886}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.7989000082015991},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.7204999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6708999872207642},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5931000113487244},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5271000266075134},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5065000057220459},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.4348999857902527},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41100001335144043},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.3982999920845032},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3637999892234802},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C28723256","wikidata":"https://www.wikidata.org/wiki/Q1400918","display_name":"Feedback vertex set","level":4,"score":0.3549000024795532},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.34529998898506165},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2915000021457672},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.2605000138282776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25920000672340393}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.30053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30053","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.30053","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30053","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Good health and well-being","score":0.8646102547645569,"id":"https://metadata.un.org/sdg/3"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Connected":[0],"Submodular":[1],"Maximization":[2],"(CSM)":[3],"is":[4,51,87,240,243],"a":[5,28,31,54,109,136,161,190,199,213,223,253,263],"graph":[6,29],"problem":[7],"with":[8,58,98,175,252,265],"important":[9],"applications":[10],"to":[11,52,111,177,272],"wireless":[12],"network":[13],"deployment,":[14],"path":[15],"planning,":[16],"epidemic":[17],"outbreaks,":[18],"and":[19,45,73,80,89,261],"cancer":[20],"genome":[21],"studies.":[22],"In":[23,83,163],"CSM,":[24,120,197],"we":[25,166],"are":[26],"given":[27],"$G$,":[30,44,57,97],"non-negative":[32],"monotone":[33],"submodular":[34],"function":[35],"$f$":[36],"on":[37,168],"subsets":[38],"of":[39,43,77,115,148,225,237,259,276],"the":[40,69,90,113,116,130,142,146,149,155,169,217,266],"vertex":[41,62,102,110],"set":[42,63,103],"an":[46,94,244],"integer":[47],"$k$.":[48],"The":[49],"goal":[50],"select":[53],"tree":[55],"in":[56,96,257,274],"$k$":[59,99,260],"edges,":[60,100],"whose":[61,101],"maximizes":[64,104],"$f$.":[65],"We":[66,138,188],"also":[67,140],"study":[68],"more":[70],"general":[71],"Directed":[72,74],"Rooted":[75],"variants":[76],"CSM":[78,174],"(DCSM":[79],"DRCSM":[81,106,247],"respectively).":[82],"both":[84],"variants,":[85],"$G$":[86],"directed":[88],"solution":[91,264],"must":[92],"be":[93,112],"out-tree":[95],"$f$;":[105],"further":[107],"specifies":[108],"root":[114],"selected":[117],"out-tree.":[118],"For":[119,208],"several":[121],"previous":[122],"works":[123],"have":[124],"proposed":[125],"polynomial":[126,132,157,191],"time":[127,133,158,192],"approximation":[128,143,171,255,269],"algorithms;":[129],"state-of-the-art":[131,156,170],"algorithm":[134,159,245,251],"achieves":[135,160,198,212],"$\u03a9(\\frac{1}{\\sqrt{k}})$-approximation.":[137],"can":[139],"parameterize":[141],"factor":[144,172,224,256,270],"by":[145,153,220],"radius":[147],"optimal":[150],"solution,":[151],"denoted":[152],"$r$;":[154],"$\u03a9(\\frac{1}{r})$-approximation.":[162],"this":[164],"paper,":[165],"improve":[167],"for":[173,195,201,229,246],"respect":[176],"$r$":[178],"as":[179,181],"well":[180],"$k$,":[182],"noting":[183],"that":[184,215,248],"$r":[185],"\\leq":[186],"k$.":[187],"propose":[189],"framework":[193,211,239],"that,":[194],"(Directed)":[196],"$\u03a9(\\frac{\\varepsilon^{3}}{{r}^{\\varepsilon}})$-approximation":[200],"every":[202,230],"constant":[203],"$\\varepsilon":[204],"\\in":[205],"(0,":[206],"1]$.":[207,233],"DRCSM,":[209],"our":[210,238],"$\u03a9(\\frac{\u03b4\\varepsilon^{3}}{{r}^{\\varepsilon}})$-approximation":[214],"violates":[216],"size":[218],"constraint":[219],"at":[221],"most":[222],"$1":[226],"+":[227],"\u03b4$":[228],"$\u03b4\\in":[231],"[\\frac{1}{k},":[232],"A":[234],"key":[235],"component":[236],"GreedyRadius,":[241],"which":[242],"takes":[249],"another":[250],"bicriteria":[254,268],"terms":[258,275],"outputs":[262],"same":[267],"(up":[271],"constants)":[273],"$r$.":[277]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-30T00:00:00"}