{"id":"https://openalex.org/W2951205595","doi":"https://doi.org/10.1137/17m1146580","title":"New Hardness Results for Routing on Disjoint Paths","display_name":"New Hardness Results for Routing on Disjoint Paths","publication_year":2020,"publication_date":"2020-12-18","ids":{"openalex":"https://openalex.org/W2951205595","doi":"https://doi.org/10.1137/17m1146580","mag":"2951205595"},"language":"en","primary_location":{"id":"doi:10.1137/17m1146580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146580","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.05429","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056023203","display_name":"Julia Chuzhoy","orcid":"https://orcid.org/0000-0001-7839-751X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Julia Chuzhoy","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027622718","display_name":"David H. K. Kim","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David H. K. Kim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056916494","display_name":"Rachit Nimavat","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rachit Nimavat","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056023203"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02054521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"2","first_page":"STOC17","last_page":"189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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/T12288","display_name":"Optimization and Search Problems","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/combinatorics","display_name":"Combinatorics","score":0.8107745051383972},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7442749738693237},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6125097870826721},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6091845631599426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6075069308280945},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6051629781723022},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5578457713127136},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5568476915359497},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5000402927398682},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4681827127933502},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4215783476829529},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10427144169807434}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8107745051383972},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7442749738693237},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6125097870826721},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6091845631599426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6075069308280945},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6051629781723022},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5578457713127136},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5568476915359497},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5000402927398682},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4681827127933502},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4215783476829529},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10427144169807434},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1146580","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1146580","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.05429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.05429","pdf_url":"https://arxiv.org/pdf/1611.05429","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:2951205595","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1611.05429.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1611.05429","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1611.05429","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.05429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.05429","pdf_url":"https://arxiv.org/pdf/1611.05429","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5195639160","display_name":null,"funder_award_id":"CCF-1616584","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8189995863","display_name":"AF: Small: Graph Routing, Vertex Sparsifiers, and Connections to Graph Theory","funder_award_id":"1616584","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8334011178","display_name":null,"funder_award_id":"CCF-1318242","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8558341523","display_name":"AF: Small: Algorithms for Graph Routing, Drawing and Partitioning","funder_award_id":"1318242","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951205595.pdf","grobid_xml":"https://content.openalex.org/works/W2951205595.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W100926944","https://openalex.org/W1989234747","https://openalex.org/W2003160050","https://openalex.org/W2005079828","https://openalex.org/W2005509629","https://openalex.org/W2011334641","https://openalex.org/W2019041817","https://openalex.org/W2019578639","https://openalex.org/W2022191808","https://openalex.org/W2035099047","https://openalex.org/W2035272561","https://openalex.org/W2060632898","https://openalex.org/W2062948942","https://openalex.org/W2064656298","https://openalex.org/W2069159763","https://openalex.org/W2081008200","https://openalex.org/W2122997342","https://openalex.org/W2140262267","https://openalex.org/W2145818650","https://openalex.org/W2148352980","https://openalex.org/W2160167461","https://openalex.org/W2171868840","https://openalex.org/W2295563127","https://openalex.org/W2401610261","https://openalex.org/W2515641369","https://openalex.org/W2949666389","https://openalex.org/W2949739362"],"related_works":["https://openalex.org/W2767782184","https://openalex.org/W2295563127","https://openalex.org/W2093083747","https://openalex.org/W2021441806","https://openalex.org/W1575996043","https://openalex.org/W2154571828","https://openalex.org/W1483343493","https://openalex.org/W2037065294","https://openalex.org/W1611628598","https://openalex.org/W2079430060","https://openalex.org/W3177347988","https://openalex.org/W1509794588","https://openalex.org/W1784825978","https://openalex.org/W1969297684","https://openalex.org/W1978693363","https://openalex.org/W1541319718","https://openalex.org/W2953179414","https://openalex.org/W2184658490","https://openalex.org/W1965636593","https://openalex.org/W2963883886"],"abstract_inverted_index":{"In":[0,150],"the":[1,7,35,40,51,67,91,98,104,120,139,146,179,197,204,211,218,225,241],"classical":[2],"Node-Disjoint":[3],"Paths":[4,222],"(NDP)":[5],"problem,":[6,223],"input":[8,99],"consists":[9],"of":[10,20,22,39,75,90,125,141,145,199,228,243],"an":[11,73,109,126],"undirected":[12],"$n$-vertex":[13],"graph":[14,100,181,185],"$G$,":[15],"and":[16,112,191],"a":[17,56,102,116,183,200,244],"collection":[18],"$\\mathcal{M}=\\{(s_1,t_1),\\ldots,(s_k,t_k)\\}$":[19],"pairs":[21,42],"its":[23],"vertices,":[24],"called":[25],"source-destination,":[26],"or":[27],"demand,":[28],"pairs.":[29],"The":[30,46,132],"goal":[31],"is":[32,53,63,72,101,115,129,148,157,182],"to":[33,160,217],"route":[34],"largest":[36],"possible":[37],"number":[38],"demand":[41],"via":[43],"node-disjoint":[44],"paths.":[45],"best":[47,68,105,121,133],"current":[48,69,106,122],"approximation":[49,61,76,123,229],"for":[50,77,232],"problem":[52,92,147],"achieved":[54],"by":[55],"simple":[57,87],"greedy":[58],"algorithm,":[59],"whose":[60],"factor":[62],"$O(\\sqrt":[64],"n)$,":[65],"while":[66],"negative":[70],"result":[71,175,216],"$\u03a9(\\log^{1/2-\u03b4}n)$-hardness":[74],"any":[78],"constant":[79],"$\u03b4$,":[80],"under":[81],"standard":[82],"complexity":[83],"assumptions.":[84],"Even":[85],"seemingly":[86],"special":[88],"cases":[89],"are":[93],"still":[94],"poorly":[95],"understood:":[96],"when":[97,113,178],"grid,":[103],"algorithm":[107,128],"achieves":[108],"$\\tilde":[110,130],"O(n^{1/4})$-approximation,":[111],"it":[114],"general":[117],"planar":[118,184,234],"graph,":[119],"ratio":[124,230],"efficient":[127],"O(n^{9/19})$.":[131],"currently":[134],"known":[135],"lower":[136],"bound":[137],"on":[138,196,240],"approximability":[140],"both":[142],"these":[143],"versions":[144],"APX-hardness.":[149],"this":[151,215],"paper":[152],"we":[153],"prove":[154],"that":[155],"NDP":[156],"$2^{\u03a9(\\sqrt{\\log":[158],"n})}$-hard":[159],"approximate,":[161],"unless":[162],"all":[163,192,237],"problems":[164],"in":[165,210],"NP":[166],"have":[167],"algorithms":[168],"with":[169,186,236],"running":[170],"time":[171],"$n^{O(\\log":[172],"n)}$.":[173],"Our":[174],"holds":[176],"even":[177,231],"underlying":[180],"maximum":[187],"vertex":[188],"degree":[189],"$3$,":[190],"source":[193],"vertices":[194,206],"lie":[195,208],"boundary":[198,242],"single":[201,245],"face":[202],"(but":[203],"destination":[205],"may":[207],"anywhere":[209],"graph).":[212],"We":[213],"extend":[214],"closely":[219],"related":[220],"Edge-Disjoint":[221],"showing":[224],"same":[226],"hardness":[227],"sub-cubic":[233],"graphs":[235],"sources":[238],"lying":[239],"face.":[246]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
