{"id":"https://openalex.org/W7083173857","doi":"https://doi.org/10.48550/arxiv.2509.18936","title":"Precoloring extension with demands on paths","display_name":"Precoloring extension with demands on paths","publication_year":2025,"publication_date":"2025-09-23","ids":{"openalex":"https://openalex.org/W7083173857","doi":"https://doi.org/10.48550/arxiv.2509.18936"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2509.18936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.18936","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2509.18936","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Das, Arun Kumar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Das, Arun Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Opler, Michal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Opler, Michal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Valla, Tom\u00e1\u0161","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Valla, Tom\u00e1\u0161","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":true,"primary_topic":{"id":"https://openalex.org/T10364","display_name":"Reproductive Biology and Fertility","score":0.3366999924182892,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10364","display_name":"Reproductive Biology and Fertility","score":0.3366999924182892,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10290","display_name":"Pregnancy and preeclampsia studies","score":0.13379999995231628,"subfield":{"id":"https://openalex.org/subfields/2729","display_name":"Obstetrics and Gynecology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10978","display_name":"Prenatal Screening and Diagnostics","score":0.04149999842047691,"subfield":{"id":"https://openalex.org/subfields/2735","display_name":"Pediatrics, Perinatology and Child Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6664999723434448},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6208000183105469},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.553600013256073},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41530001163482666},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.4104999899864197},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4099000096321106},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.40450000762939453},{"id":"https://openalex.org/keywords/fractional-coloring","display_name":"Fractional coloring","score":0.4016999900341034},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38499999046325684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7013000249862671},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6208000183105469},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.553600013256073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5485000014305115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5030999779701233},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41530001163482666},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.4104999899864197},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.4016999900341034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.37959998846054077},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.3050999939441681},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.2946000099182129},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.2921999990940094},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.2694000005722046},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2509.18936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.18936","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2509.18936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.18936","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"$G$":[1,43],"be":[2,14],"a":[3,6,22,39,94,127,177,233,275],"graph":[4],"with":[5,32,101,151],"set":[7,23],"of":[8,24,42,58,65,68,80,141,163,181,203,222,246,253],"precolored":[9,60,133,164,254],"vertices,":[10,61],"and":[11,21,76,106,125,144,160,187,224,250],"let":[12],"us":[13],"given":[15],"an":[16,146,152],"integer":[17,25],"distance":[18,64],"parameter":[19,235],"$d$":[20,159],"demands":[26],"$d_1,\\dots,d_c$.":[27],"The":[28],"Distance":[29,171,265,284],"Precoloring":[30,172,266],"Extension":[31,173,267],"Demands":[33],"(DPED)":[34],"problem":[35,90,114,174,212,287],"is":[36,72,86,91,191,215,268],"to":[37,111,137],"compute":[38],"vertex":[40],"$c$-coloring":[41],"such":[44],"that":[45,169,209,264],"the":[46,52,56,59,63,69,78,112,138,142,161,170,184,200,210,220,225,228,244,248,251,259,272,283],"following":[47],"three":[48],"conditions":[49],"hold:":[50],"(i)":[51],"resulting":[53],"coloring":[54],"respects":[55],"colors":[57,223],"(ii)":[62],"two":[66,139],"vertices":[67,81,134,255],"same":[70],"color":[71,84],"at":[73],"least":[74],"$d$,":[75],"(iii)":[77],"number":[79,162,221,245,252],"colored":[82],"by":[83,93,158,194,219,271],"$i$":[85],"exactly":[87],"$d_i$.":[88],"This":[89],"motivated":[92],"program":[95],"scheduling":[96],"in":[97],"commercial":[98],"broadcast":[99],"channels":[100],"constraints":[102],"on":[103,123,175,205,213,241,288],"content":[104],"repetition":[105],"placement,":[107],"which":[108],"leads":[109],"precisely":[110],"DPED":[113,122,150,182,189,204,211,240],"for":[115,149,239,282],"paths.":[116,206,289],"In":[117],"this":[118,195],"paper,":[119],"we":[120,167,197,231,262,277],"study":[121,199],"paths":[124,214,242],"present":[126],"polynomial":[128],"time":[129],"exact":[130],"algorithm":[131,148,238],"when":[132,217,243],"are":[135,256],"restricted":[136],"ends":[140],"path":[143],"devise":[145,232],"approximation":[147,154],"additive":[153],"factor":[155],"polynomially":[156],"bounded":[157],"vertices.":[165],"Then,":[166],"prove":[168,263],"paths,":[176],"less":[178],"restrictive":[179],"version":[180],"without":[183],"demand":[185],"constraints,":[186],"then":[188],"itself,":[190],"NP-complete.":[192],"Motivated":[193],"result,":[196],"further":[198],"parameterized":[201,218,270],"complexity":[202],"We":[207],"establish":[208],"$W[1]$-hard":[216],"distance.":[226,273],"On":[227],"positive":[229],"side,":[230],"fixed":[234],"tractable":[236],"(FPT)":[237],"colors,":[247],"distance,":[249],"considered":[257],"as":[258],"parameters.":[260],"Moreover,":[261],"FPT":[269],"As":[274],"byproduct,":[276],"also":[278],"obtain":[279],"several":[280],"results":[281],"List":[285],"Coloring":[286]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}