{"id":"https://openalex.org/W1988645484","doi":"https://doi.org/10.1137/s0895480196312334","title":"Compact Representations of Cuts","display_name":"Compact Representations of Cuts","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1988645484","doi":"https://doi.org/10.1137/s0895480196312334","mag":"1988645484"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480196312334","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480196312334","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5079559219","display_name":"David Hartvigsen","orcid":"https://orcid.org/0000-0001-8353-5577"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David Hartvigsen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079559219"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.11609991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"14","issue":"1","first_page":"49","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8600821495056152},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7909642457962036},{"id":"https://openalex.org/keywords/minimum-cut","display_name":"Minimum cut","score":0.5646921396255493},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48902592062950134},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48192644119262695},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.46816393733024597}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8600821495056152},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7909642457962036},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.5646921396255493},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48902592062950134},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48192644119262695},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.46816393733024597}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480196312334","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480196312334","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W41039768","https://openalex.org/W82387719","https://openalex.org/W1524804355","https://openalex.org/W1969525246","https://openalex.org/W1975896992","https://openalex.org/W1983096342","https://openalex.org/W1986207529","https://openalex.org/W1995818744","https://openalex.org/W1996453957","https://openalex.org/W2001558518","https://openalex.org/W2001646664","https://openalex.org/W2031248452","https://openalex.org/W2035228443","https://openalex.org/W2041131084","https://openalex.org/W2057463094","https://openalex.org/W2114552889","https://openalex.org/W2115049345","https://openalex.org/W2121204510","https://openalex.org/W2127631842","https://openalex.org/W2150815458","https://openalex.org/W2152986618","https://openalex.org/W2167637346","https://openalex.org/W2338905098","https://openalex.org/W2405419040","https://openalex.org/W3139666781","https://openalex.org/W3145896515","https://openalex.org/W3150574672","https://openalex.org/W4213064273"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W4288278856","https://openalex.org/W2572370460","https://openalex.org/W1976691234"],"abstract_inverted_index":{"Consider":[0],"the":[1,53,61,125,170,177,209],"${n}\\choose{2}$":[2],"(or":[3,136,156],"$O(n^{2})$)":[4],"min-cut":[5,65,85],"problems":[6],"on":[7,101],"a":[8,42,64,97,102,105,112,119,130,163,180],"graph":[9],"with":[10,52,169],"n":[11],"nodes":[12,127],"and":[13,18,227],"nonnegative":[14],"edge":[15],"weights.":[16],"Gomory":[17],"Hu":[19],"[J.":[20],"Soc.":[21],"Indust.":[22],"Appl.":[23],"Math.,":[24],"9":[25,223],"(1961),":[26],"pp.":[27,146,218,225,235],"551--570]":[28],"showed":[29,74,148],"(essentially)":[30,149],"that":[31,122,150],"there":[32,151],"are":[33,134,152],"at":[34,153],"most":[35,154],"n-1":[36,84],"different":[37,131,158],"min-cuts.":[38],"They":[39],"also":[40,190],"described":[41],"compact":[43,164],"structure":[44,77,165,194],"(the":[45],"flow":[46],"equivalent":[47],"tree)":[48],"of":[49,59,63,91,108,116,124,166,179,211],"size":[50,167],"O(n)":[51],"following":[54,171],"property:":[55,172],"for":[56,104,173],"any":[57,174],"pair":[58],"nodes,":[60,110,176],"value":[62,178],"can":[66,78,183,195],"be":[67,79,184,196],"obtained":[68,185],"from":[69,186],"this":[70,76,187,193],"structure.":[71,188],"Furthermore,":[72],"they":[73],"how":[75,192],"found":[80,197],"by":[81,198],"solving":[82,199],"only":[83,200],"problems.":[86,139,204],"This":[87,205],"paper":[88],"contains":[89],"generalizations":[90],"these":[92],"results.":[93],"For":[94],"example,":[95],"consider":[96],"k-terminal":[98,202],"cut":[99,203],"problem":[100],"graph:":[103],"given":[106],"set":[107,115],"k":[109,126,175],"delete":[111],"minimum":[113],"weight":[114],"edges":[117],"(called":[118],"k-cut)":[120],"so":[121],"each":[123],"is":[128],"in":[129,230],"component.":[132],"There":[133],"${n}\\choose{k}$":[135],"O(nk))":[137],"such":[138],"Hassin":[140,212],"[Math.":[141,213],"Oper.":[142,214],"Res.,":[143,215],"13":[144,216],"(1988),":[145,217],"535--542]":[147],"${n-1}\\choose{k-1}$":[155,201],"O(nk-1))":[157],"min":[159,181],"k-cuts.":[160],"We":[161,189],"describe":[162],"O(nk-1)":[168],"k-cut":[182],"show":[191],"work":[206],"builds":[207],"upon":[208],"results":[210],"535--542],":[219],"[Oper.":[220],"Res.":[221],"Lett.,":[222],"(1990),":[224],"315--318],":[226],"[Lecture":[228],"Notes":[229],"Comput.":[231],"Sci.":[232],"450,":[233],"1990,":[234],"228--299].":[236]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
