{"id":"https://openalex.org/W7125501768","doi":"https://doi.org/10.1145/3790095","title":"Cut Paths and Their Remainder Structure","display_name":"Cut Paths and Their Remainder Structure","publication_year":2026,"publication_date":"2026-01-23","ids":{"openalex":"https://openalex.org/W7125501768","doi":"https://doi.org/10.1145/3790095"},"language":"en","primary_location":{"id":"doi:10.1145/3790095","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3790095","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007584366","display_name":"Massimo Cairo","orcid":"https://orcid.org/0000-0001-7247-756X"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Massimo Cairo","raw_affiliation_strings":["Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":"https://orcid.org/0000-0001-7247-756X","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014870050","display_name":"Shahbaz Khan","orcid":"https://orcid.org/0000-0001-9352-0088"},"institutions":[{"id":"https://openalex.org/I154851008","display_name":"Indian Institute of Technology Roorkee","ror":"https://ror.org/00582g326","country_code":"IN","type":"education","lineage":["https://openalex.org/I154851008"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shahbaz Khan","raw_affiliation_strings":["Department of Computer Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India"],"raw_orcid":"https://orcid.org/0000-0001-9352-0088","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India","institution_ids":["https://openalex.org/I154851008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061874157","display_name":"Rom\u00e9o Rizzi","orcid":"https://orcid.org/0000-0002-2387-0952"},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Romeo Rizzi","raw_affiliation_strings":["Department of Computer Science, University of Verona, Verona, Italy"],"raw_orcid":"https://orcid.org/0000-0002-2387-0952","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Verona, Verona, Italy","institution_ids":["https://openalex.org/I119439378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025072151","display_name":"Sebastian Schmidt","orcid":"https://orcid.org/0000-0003-4878-2809"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Sebastian Schmidt","raw_affiliation_strings":["Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":"https://orcid.org/0000-0003-4878-2809","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063897224","display_name":"Alexandru I. Tomescu","orcid":"https://orcid.org/0000-0002-5747-8350"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Alexandru I. Tomescu","raw_affiliation_strings":["Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":"https://orcid.org/0000-0002-5747-8350","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008708532","display_name":"Elia C. Zirondelli","orcid":"https://orcid.org/0000-0001-5302-0580"},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]},{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Elia C. Zirondelli","raw_affiliation_strings":["University of Trento, Trento, Italy and University of Verona, Verona, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5302-0580","affiliations":[{"raw_affiliation_string":"University of Trento, Trento, Italy and University of Verona, Verona, Italy","institution_ids":["https://openalex.org/I119439378","https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1218223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"2","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.5964999794960022,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.5964999794960022,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.06629999727010727,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.06440000236034393,"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/remainder","display_name":"Remainder","score":0.9168999791145325},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9052000045776367},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.545799970626831},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5393000245094299},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5210999846458435},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5130000114440918},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5066999793052673},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4375},{"id":"https://openalex.org/keywords/minimum-cut","display_name":"Minimum cut","score":0.41269999742507935}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.9168999791145325},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9052000045776367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7008000016212463},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5393000245094299},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5210999846458435},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5130000114440918},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5115000009536743},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5066999793052673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48410001397132874},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4375},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.398499995470047},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.3885999917984009},{"id":"https://openalex.org/C5134670","wikidata":"https://www.wikidata.org/wiki/Q1626444","display_name":"Cut","level":4,"score":0.3750999867916107},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32420000433921814},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.302700012922287},{"id":"https://openalex.org/C171528893","wikidata":"https://www.wikidata.org/wiki/Q5121450","display_name":"Circle graph","level":5,"score":0.30070000886917114},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C22251595","wikidata":"https://www.wikidata.org/wiki/Q670036","display_name":"Arc length","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.25999999046325684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25699999928474426},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3790095","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3790095","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2831577090","display_name":null,"funder_award_id":"ERC, SCALEBIO, 101169716","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G658116447","display_name":null,"funder_award_id":"346968, 358744","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1880391707","https://openalex.org/W2001331197","https://openalex.org/W2011379509","https://openalex.org/W2032370604","https://openalex.org/W2061687898","https://openalex.org/W2078331392","https://openalex.org/W2090526848","https://openalex.org/W2099964107","https://openalex.org/W2118382442","https://openalex.org/W2535388830","https://openalex.org/W2621577171","https://openalex.org/W2792957821","https://openalex.org/W2965565043","https://openalex.org/W3017318380","https://openalex.org/W3043435921","https://openalex.org/W3082938733","https://openalex.org/W3104459592","https://openalex.org/W3207959194","https://openalex.org/W4288077753","https://openalex.org/W4380786948"],"related_works":[],"abstract_inverted_index":{"Cut":[0,210],"arcs":[1],",":[2,6,27,44,71,84,115],"or":[3,223],"strong":[4],"bridges":[5],"are":[7],"one":[8],"of":[9,107,144,188,193,206,229,232,235],"the":[10,255],"most":[11,139,147],"fundamental":[12],"reachability":[13,172],"notions":[14],"in":[15,19,239,249,259],"directed":[16],"graphs.":[17],"Specifically,":[18],"a":[20,30,121,128,135,186,194,219,236],"strongly":[21,195],"connected":[22,196],"graph":[23,136],"\\(G=(V,E)\\)":[24],"(":[25],"\\(|V|=n\\)":[26],"\\(|E|=m\\)":[28],"),":[29],"cut":[31,69,108,129,142,159,163,237],"arc":[32,35],"is":[33,180,185,199,221],"an":[34,152],"\\(e\\in":[36],"E\\)":[37],"for":[38,78,127,157],"which":[39,79,116],"there":[40,80],"exist":[41,81],"\\(u,v\\in":[42,82],"V\\)":[43,83],"such":[45,85],"that":[46,72,86,134],"all":[47,87,233,245],"\\(":[48,52,57,75,88,92,97],"u":[49,89],"\\)":[50,54,59,77,90,94,99],"-":[51,91],"v":[53,93],"walks":[55,74,95,208,248],"contain":[56,96],"e":[58],".":[60,263],"In":[61],"this":[62,66],"article,":[63],"we":[64,117,242],"generalise":[65],"notion":[67],"to":[68,119,169],"paths":[70,109,143,164,211],"is,":[73],"W":[76,98],"as":[100,176],"subwalk.":[101],"We":[102,131,161],"first":[103],"prove":[104],"various":[105],"properties":[106],"and":[110,150,165],"define":[111],"their":[112,166],"remainder":[113,167,230],"structure":[114,168],"use":[118],"present":[120,151],"simple":[122,213],"\\(O(m)\\)":[123,214],"-time":[124,215],"verification":[125],"algorithm":[126,156,257],"path.":[130],"further":[132],"show":[133],"contains":[137],"at":[138,146],"\\(O(n)\\)":[140,148],"maximal":[141,158,246],"length":[145],"each,":[149],"optimal":[153],"\\(O(n^{2})\\)":[154],"enumeration":[155],"paths.":[160],"apply":[162],"improve":[170],"several":[171],"problems":[173],"from":[174],"bioinformatics,":[175],"follows.":[177],"A":[178],"walk":[179,192,220],"called":[181],"safe":[182,222],"if":[183,218],"it":[184],"subwalk":[187],"every":[189],"node-covering":[190,204],"closed":[191,207],"graph.":[197],"Multi-safety":[198],"defined":[200],"analogously,":[201],"by":[202,226],"considering":[203],"sets":[205],"instead.":[209],"provide":[212],"algorithms":[216],"verifying":[217],"multi-safe.":[224],"Further,":[225],"simultaneous":[227],"computation":[228],"structures":[231],"subwalks":[234],"path":[238],"linear":[240],"time,":[241],"can":[243],"identify":[244],"multi-safe":[247],"\\(O(mn)\\)":[250],"time.":[251],"This":[252],"improves":[253],"over":[254],"state-of-the-art":[256],"running":[258],"time":[260],"\\(O(m^{2}+n^{3}\\log":[261],"n)\\)":[262]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2026-01-24T00:00:00"}