{"id":"https://openalex.org/W2097053246","doi":"https://doi.org/10.1145/2462356.2462366","title":"Counting and sampling minimum cuts in genus g graphs","display_name":"Counting and sampling minimum cuts in genus g graphs","publication_year":2013,"publication_date":"2013-06-17","ids":{"openalex":"https://openalex.org/W2097053246","doi":"https://doi.org/10.1145/2462356.2462366","mag":"2097053246"},"language":"en","primary_location":{"id":"doi:10.1145/2462356.2462366","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2462356.2462366","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-ninth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","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/A5011219239","display_name":"Erin Wolf Chambers","orcid":"https://orcid.org/0000-0001-8333-3676"},"institutions":[{"id":"https://openalex.org/I47838141","display_name":"Saint Louis University","ror":"https://ror.org/01p7jjy08","country_code":"US","type":"education","lineage":["https://openalex.org/I47838141"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erin W. Chambers","raw_affiliation_strings":["Saint Louis University, St. Louis, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saint Louis University, St. Louis, MO, USA","institution_ids":["https://openalex.org/I47838141"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013518909","display_name":"Kyle Fox","orcid":"https://orcid.org/0000-0002-2446-8594"},"institutions":[{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kyle Fox","raw_affiliation_strings":["University of Illinois, Urbana, IL, USA","University of Illinois Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I2801919071"]},{"raw_affiliation_string":"University of Illinois Urbana, IL, USA","institution_ids":["https://openalex.org/I2801919071"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024487390","display_name":"Amir Nayyeri","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amir Nayyeri","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, Pa., USA#TAB#","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5447,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59685039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"249","last_page":"258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9993000030517578,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9708999991416931,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.7690682411193848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6816419363021851},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.548378050327301},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.5226675868034363},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5060314536094666},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5043033361434937},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.45208656787872314},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.4179295301437378},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29106923937797546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16890713572502136}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7690682411193848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6816419363021851},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.548378050327301},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.5226675868034363},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5060314536094666},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5043033361434937},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.45208656787872314},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.4179295301437378},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29106923937797546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16890713572502136},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/2462356.2462366","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2462356.2462366","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-ninth annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.5946","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.5946","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mathcs.slu.edu/~chambers/papers/counting-cuts.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.357.4388","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.357.4388","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.engr.illinois.edu/~kylefox2/publications/counting-cuts.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.468.44","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.468.44","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mathcs.slu.edu/~chambers/papers/counting-cuts.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.685.8765","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.685.8765","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.engr.illinois.edu/%7Ekylefox2/publications/counting-cuts.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.712.5969","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.712.5969","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kylejfox.com/publications/counting-cuts.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W48526783","https://openalex.org/W60423602","https://openalex.org/W594463866","https://openalex.org/W1507614398","https://openalex.org/W1510135378","https://openalex.org/W1522210445","https://openalex.org/W1523441917","https://openalex.org/W1527270374","https://openalex.org/W1572973141","https://openalex.org/W1607394607","https://openalex.org/W1836357517","https://openalex.org/W1874894208","https://openalex.org/W1969523663","https://openalex.org/W1974358136","https://openalex.org/W1980889962","https://openalex.org/W1983383464","https://openalex.org/W1987197912","https://openalex.org/W1988593903","https://openalex.org/W1994931826","https://openalex.org/W1995473411","https://openalex.org/W1998076865","https://openalex.org/W2002531683","https://openalex.org/W2006152944","https://openalex.org/W2008597108","https://openalex.org/W2009879748","https://openalex.org/W2016588822","https://openalex.org/W2021547908","https://openalex.org/W2023808821","https://openalex.org/W2024420212","https://openalex.org/W2030509174","https://openalex.org/W2039086323","https://openalex.org/W2039305125","https://openalex.org/W2046021036","https://openalex.org/W2047861451","https://openalex.org/W2049188514","https://openalex.org/W2060075372","https://openalex.org/W2064175146","https://openalex.org/W2066108505","https://openalex.org/W2067431706","https://openalex.org/W2068595367","https://openalex.org/W2076735064","https://openalex.org/W2078191188","https://openalex.org/W2078443814","https://openalex.org/W2083049364","https://openalex.org/W2090359754","https://openalex.org/W2092904196","https://openalex.org/W2097289283","https://openalex.org/W2102883744","https://openalex.org/W2103099082","https://openalex.org/W2106352538","https://openalex.org/W2113679823","https://openalex.org/W2120424341","https://openalex.org/W2126169066","https://openalex.org/W2147510331","https://openalex.org/W2159332695","https://openalex.org/W2199785256","https://openalex.org/W2465715994","https://openalex.org/W2622918074","https://openalex.org/W2762935521","https://openalex.org/W2963816213","https://openalex.org/W3040586665","https://openalex.org/W3104625577","https://openalex.org/W3140579943","https://openalex.org/W4213060883","https://openalex.org/W4319589071","https://openalex.org/W6643783730","https://openalex.org/W6792131838"],"related_works":["https://openalex.org/W2052299349","https://openalex.org/W1901944325","https://openalex.org/W4297728441","https://openalex.org/W4388094543","https://openalex.org/W2997069702","https://openalex.org/W4380487890","https://openalex.org/W4292953838","https://openalex.org/W4288263214","https://openalex.org/W2967221944","https://openalex.org/W2094500233"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2],"a":[3,42,58,109],"directed":[4],"graph":[5],"with":[6,17,89],"n":[7],"vertices":[8,20],"embedded":[9],"on":[10],"an":[11,70,95],"orientable":[12],"surface":[13],"of":[14,55],"genus":[15],"g":[16],"two":[18],"designated":[19],"s":[21],"and":[22,86],"t.":[23],"We":[24,92],"show":[25],"that":[26,81],"counting":[27,53],"the":[28],"minimum":[29,104,110],"(s,t)-cuts":[30],"in":[31,37,57,73,115],"G":[32],"is":[33,69],"fixed":[34,83],"parameter":[35,84],"tractable":[36,85],"g.":[38],"Specially,":[39],"we":[40,64],"give":[41],"2O(g)":[43],"n2":[44],"time":[45,117],"algorithm":[46,51,96,101],"for":[47],"this":[48],"problem.":[49],"Our":[50],"requires":[52],"sets":[54],"cycles":[56,68],"particular":[59],"integer":[60,90],"homology":[61],"class.":[62],"That":[63],"can":[65,107],"count":[66,103],"these":[67],"interesting":[71],"result":[72],"itself":[74],"as":[75],"there":[76],"are":[77,82],"few":[78],"prior":[79],"results":[80],"deal":[87],"directly":[88],"homology.":[91],"also":[93],"describe":[94],"which,":[97],"after":[98],"running":[99],"our":[100],"to":[102],"cuts":[105],"once,":[106],"sample":[108],"cut":[111],"uniformly":[112],"at":[113],"random":[114],"O(gn)":[116],"per":[118],"sample.":[119]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
