{"id":"https://openalex.org/W2086904111","doi":"https://doi.org/10.1145/1250790.1250882","title":"Vertex cuts, random walks, and dimension reduction in series-parallel graphs","display_name":"Vertex cuts, random walks, and dimension reduction in series-parallel graphs","publication_year":2007,"publication_date":"2007-06-11","ids":{"openalex":"https://openalex.org/W2086904111","doi":"https://doi.org/10.1145/1250790.1250882","mag":"2086904111"},"language":"en","primary_location":{"id":"doi:10.1145/1250790.1250882","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","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/A5025420692","display_name":"Bo Brinkman","orcid":"https://orcid.org/0000-0003-2951-2141"},"institutions":[{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]},{"id":"https://openalex.org/I83328450","display_name":"Miami University","ror":"https://ror.org/05nbqxr67","country_code":"US","type":"education","lineage":["https://openalex.org/I83328450"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bo Brinkman","raw_affiliation_strings":["Miami University, Miami, OH","Miami University, Miami, OH#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Miami University, Miami, OH","institution_ids":["https://openalex.org/I83328450"]},{"raw_affiliation_string":"Miami University, Miami, OH#TAB#","institution_ids":["https://openalex.org/I145608581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057049738","display_name":"Adriana Karagiozova","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adriana Karagiozova","raw_affiliation_strings":["Princeton University, Princeton, NJ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028879014","display_name":"James R. Lee","orcid":"https://orcid.org/0000-0002-3512-1617"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James R. Lee","raw_affiliation_strings":["University of Washington, Seattle, WA","University Of Washington (Seattle, WA)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington, Seattle, WA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"University Of Washington (Seattle, WA)","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6069,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85588972,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"621","last_page":"630"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9969000220298767,"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":0.9966999888420105,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.7210955619812012},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.6373169422149658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5834664106369019},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.576086699962616},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5672189593315125},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5042241811752319},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48932546377182007},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4871959090232849},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4769412577152252},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.45714572072029114},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.44251111149787903},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4328887462615967},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3807315230369568},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33185330033302307},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2421935498714447},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14832186698913574},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.11498546600341797},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0713895857334137}],"concepts":[{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.7210955619812012},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6373169422149658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5834664106369019},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.576086699962616},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5672189593315125},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5042241811752319},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48932546377182007},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4871959090232849},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4769412577152252},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.45714572072029114},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.44251111149787903},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4328887462615967},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3807315230369568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33185330033302307},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2421935498714447},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14832186698913574},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.11498546600341797},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0713895857334137},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1250790.1250882","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.5302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.5302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.washington.edu/homes/jrl/papers/p621-lee.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":34,"referenced_works":["https://openalex.org/W48861618","https://openalex.org/W1484819834","https://openalex.org/W1523004878","https://openalex.org/W1526777878","https://openalex.org/W1530239281","https://openalex.org/W1541617071","https://openalex.org/W1594954118","https://openalex.org/W1968333148","https://openalex.org/W1981853164","https://openalex.org/W1984672232","https://openalex.org/W2001075173","https://openalex.org/W2004322147","https://openalex.org/W2007806267","https://openalex.org/W2010832227","https://openalex.org/W2020632401","https://openalex.org/W2049609719","https://openalex.org/W2063491776","https://openalex.org/W2070208264","https://openalex.org/W2076164610","https://openalex.org/W2083854723","https://openalex.org/W2097636047","https://openalex.org/W2127114399","https://openalex.org/W2127248062","https://openalex.org/W2141793995","https://openalex.org/W2149463264","https://openalex.org/W2154876245","https://openalex.org/W2167061810","https://openalex.org/W2167816765","https://openalex.org/W2169071224","https://openalex.org/W2176446742","https://openalex.org/W2576544140","https://openalex.org/W2962980142","https://openalex.org/W4291439952","https://openalex.org/W6750326706"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W3024211597","https://openalex.org/W2951046662","https://openalex.org/W1964113132","https://openalex.org/W46292265","https://openalex.org/W1561846021","https://openalex.org/W1554245510","https://openalex.org/W2046834193"],"abstract_inverted_index":{"We":[0,44],"consider":[1],"questions":[2],"about":[3],"vertex":[4],"cuts":[5],"in":[6,10,16],"graphs,":[7,55],"random":[8],"walks":[9],"metric":[11,42],"spaces,":[12],"and":[13,18,56],"dimension":[14],"reduction":[15],"L1":[17],"L2;":[19],"these":[20,46],"topics":[21],"are":[22],"intimately":[23],"connected":[24],"because":[25],"they":[26],"can":[27],"each":[28],"be":[29],"reduced":[30],"to":[31],"the":[32,49],"existence":[33],"ofvarious":[34],"families":[35],"of":[36,51,63],"real-valued":[37],"Lipschitz":[38],"maps":[39],"on":[40],"certain":[41],"spaces.":[43],"view":[45],"issues":[47],"through":[48],"lens":[50],"shortest-path":[52],"metricson":[53],"series-parallel":[54],"we":[57],"discussthe":[58],"implications":[59],"for":[60],"a":[61],"variety":[62],"well-known":[64],"open":[65],"problems.":[66],"Our":[67],"main":[68],"results":[69],"follow.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
