{"id":"https://openalex.org/W4415329176","doi":"https://doi.org/10.4230/lipics.sand.2026.4","title":"Families of Tractable Problems with Respect to Vertex-Interval-Membership Width and Its Generalisations","display_name":"Families of Tractable Problems with Respect to Vertex-Interval-Membership Width and Its Generalisations","publication_year":2025,"publication_date":"2025-05-21","ids":{"openalex":"https://openalex.org/W4415329176","doi":"https://doi.org/10.4230/lipics.sand.2026.4"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.15699","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.15699","pdf_url":"https://arxiv.org/pdf/2505.15699","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.15699","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014039487","display_name":"Jessica Enright","orcid":"https://orcid.org/0000-0002-0266-3292"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Enright, Jessica","raw_affiliation_strings":["School of Computing Science, University of Glasgow, UK"],"raw_orcid":"https://orcid.org/0000-0002-0266-3292","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, UK","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109712003","display_name":"Samuel D. Hand","orcid":null},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hand, Samuel D.","raw_affiliation_strings":["School of Computing Science, University of Glasgow, UK"],"raw_orcid":"https://orcid.org/0000-0001-8021-249X","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, UK","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092160873","display_name":"Laura Larios-Jones","orcid":"https://orcid.org/0000-0003-3322-0176"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Larios-Jones, Laura","raw_affiliation_strings":["School of Computing Science, University of Glasgow, UK"],"raw_orcid":"https://orcid.org/0000-0003-3322-0176","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, UK","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088807601","display_name":"Kitty Meeks","orcid":"https://orcid.org/0000-0001-5299-3073"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Meeks, Kitty","raw_affiliation_strings":["School of Computing Science, University of Glasgow, UK"],"raw_orcid":"https://orcid.org/0000-0001-5299-3073","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, UK","institution_ids":["https://openalex.org/I7882870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I7882870"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T13234","display_name":"advanced mathematical theories","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"advanced mathematical theories","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9232000112533569,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9168999791145325,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4661000072956085},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4090000092983246},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.38609999418258667},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.38519999384880066},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.383899986743927},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.3569999933242798},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.35580000281333923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5458999872207642},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4228000044822693},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4052000045776367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3896999955177307},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3831999897956848},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37869998812675476},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.29510000348091125},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.25290000438690186},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:2505.15699","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.15699","pdf_url":"https://arxiv.org/pdf/2505.15699","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.gla.ac.uk:385052","is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/view/author/28436.html>","pdf_url":"https://eprints.gla.ac.uk/385052/2/385052.pdf","source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Proceedings"},{"id":"pmh:doi:10.4230/lipics.sand.2026.4","is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/269008/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"pmh:oai:drops-oai.dagstuhl.de:26238","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.4","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"doi:10.48550/arxiv.2505.15699","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.15699","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"},{"id":"doi:10.4230/lipics.sand.2026.4","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.sand.2026.4","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.15699","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.15699","pdf_url":"https://arxiv.org/pdf/2505.15699","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4226183444","display_name":"Beyond One Solution in Combinatorial Optimisation","funder_award_id":"EP/V032305/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7222129398","display_name":"Multilayer Algorithmics to Leverage Graph Structure (MultilayerALGS)","funder_award_id":"EP/T004878/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415329176.pdf","grobid_xml":"https://content.openalex.org/works/W4415329176.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Temporal":[0],"graphs":[1,3,31],"are":[2,6,13,89],"whose":[4],"edges":[5],"labelled":[7],"with":[8,41,154],"times":[9],"at":[10,79],"which":[11,51,119],"they":[12],"active.":[14],"Their":[15],"time-sensitivity":[16],"provides":[17],"a":[18,66,94,148],"useful":[19],"model":[20],"of":[21,71,78,129,150,166],"real":[22],"networks,":[23],"but":[24],"renders":[25],"many":[26,85],"problems":[27,53,151],"studied":[28],"on":[29,68],"temporal":[30,52,164],"more":[32],"computationally":[33],"complex":[34],"than":[35],"their":[36],"static":[37],"counterparts.":[38],"To":[39],"contend":[40],"this,":[42,145],"there":[43],"has":[44],"been":[45],"recent":[46],"work":[47],"devising":[48],"parameters":[49],"for":[50,113,126,140],"become":[54],"tractable.":[55],"One":[56],"such":[57],"parameter":[58],"is":[59],"vertex-interval-membership":[60],"(VIM)":[61],"width.":[62],"Broadly,":[63],"this":[64],"gives":[65],"bound":[67],"the":[69,132],"number":[70],"vertices":[72],"we":[73,92,110,146],"need":[74,133],"to":[75,83,123,134,156,163,175],"keep":[76],"track":[77],"any":[80],"given":[81],"time":[82],"solve":[84],"problems.":[86],"Our":[87],"contributions":[88],"two-fold.":[90],"Firstly,":[91],"introduce":[93],"new":[95],"parameter,":[96],"tree-interval-membership":[97],"(TIM)":[98],"width,":[99],"that":[100],"generalises":[101],"both":[102,114,157],"VIM":[103,115],"width":[104,118],"and":[105,116,172],"several":[106],"existing":[107],"generalisations.":[108],"Secondly,":[109],"provide":[111,147],"meta-algorithms":[112],"TIM":[117],"can":[120],"be":[121],"used":[122],"prove":[124],"fixed-parameter-tractability":[125],"large":[127],"families":[128],"problems,":[130],"bypassing":[131],"give":[135],"involved":[136],"dynamic":[137],"programming":[138],"arguments":[139],"every":[141],"problem.":[142],"In":[143],"doing":[144],"characterisation":[149],"in":[152],"FPT":[153],"respect":[155],"parameters.":[158],"We":[159],"apply":[160],"these":[161],"algorithms":[162],"versions":[165],"Hamiltonian":[167],"path,":[168],"dominating":[169],"set,":[170],"matching,":[171],"edge":[173],"deletion":[174],"limit":[176],"maximum":[177],"reachability.":[178]},"counts_by_year":[],"updated_date":"2026-07-16T13:24:37.021932","created_date":"2025-10-19T00:00:00"}
