{"id":"https://openalex.org/W2783504746","doi":"https://doi.org/10.1109/allerton.2017.8262861","title":"Efficiently finding all power flow solutions to tree networks","display_name":"Efficiently finding all power flow solutions to tree networks","publication_year":2017,"publication_date":"2017-10-01","ids":{"openalex":"https://openalex.org/W2783504746","doi":"https://doi.org/10.1109/allerton.2017.8262861","mag":"2783504746"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2017.8262861","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-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/A5025653275","display_name":"Alisha Zachariah","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alisha Zachariah","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, WI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034877995","display_name":"Zachary Charles","orcid":"https://orcid.org/0000-0001-8997-874X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zachary Charles","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, WI, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025653275"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.1433,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54151982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1107","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10305","display_name":"Power System Optimization and Stability","score":0.995199978351593,"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"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9409000277519226,"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/tree","display_name":"Tree (set theory)","score":0.6431905031204224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5216936469078064},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.48725786805152893},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4823412597179413},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.473949670791626},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.4633956551551819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4554968476295471},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.44490766525268555},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.43524011969566345},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11151733994483948},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.09409543871879578}],"concepts":[{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6431905031204224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5216936469078064},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.48725786805152893},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4823412597179413},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.473949670791626},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.4633956551551819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4554968476295471},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.44490766525268555},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.43524011969566345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11151733994483948},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.09409543871879578},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2017.8262861","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262861","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338284","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W571101512","https://openalex.org/W1976231053","https://openalex.org/W2028576930","https://openalex.org/W2055858792","https://openalex.org/W2055964119","https://openalex.org/W2057057063","https://openalex.org/W2111198155","https://openalex.org/W2118525742","https://openalex.org/W2131916861","https://openalex.org/W2135514263","https://openalex.org/W2153332004","https://openalex.org/W2153464144","https://openalex.org/W2165164291","https://openalex.org/W2171845477","https://openalex.org/W2337490698","https://openalex.org/W2964133375","https://openalex.org/W4234426551","https://openalex.org/W4246867982"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2047547195","https://openalex.org/W204175656","https://openalex.org/W2911841387","https://openalex.org/W2803255289","https://openalex.org/W1512294453","https://openalex.org/W1993992974","https://openalex.org/W2550734047","https://openalex.org/W1998550351","https://openalex.org/W4296157159"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,109],"present":[4],"an":[5],"algorithm":[6,22,43,63,83,112,133],"which":[7],"provably":[8],"finds":[9],"all":[10,118],"voltage":[11,119],"solutions":[12,99],"to":[13,26,30,51,102,113,116],"the":[14,28,36,39,45,49,59,62,66,69,72,89,95,103,139,149],"power":[15],"flow":[16],"equations":[17,29],"on":[18,65],"tree":[19,50],"networks.":[20],"Our":[21],"uses":[23],"elimination":[24],"theory":[25],"reduce":[27],"univariate":[31],"polynomials":[32],"whose":[33],"roots":[34],"govern":[35],"voltages":[37],"of":[38,48,61,68,97,105,151],"entire":[40],"tree.":[41,73],"The":[42],"utilizes":[44],"sparse":[46],"structure":[47],"decrease":[52],"its":[53],"computational":[54],"cost.":[55],"We":[56,129],"show":[57,130],"that":[58,76,131],"runtime":[60],"depends":[64],"degrees":[67],"vertices":[70],"in":[71,77,88,138],"This":[74],"implies":[75],"physically":[78],"motivated":[79],"distribution":[80],"networks,":[81],"our":[82,111,132],"runs":[84],"much":[85],"faster":[86],"than":[87],"worst-case":[90],"scenario,":[91],"scaling":[92],"more":[93],"like":[94],"number":[96,104,150],"real":[98],"as":[100],"opposed":[101],"complex":[106],"solutions.":[107],"Finally,":[108],"compare":[110],"common":[114],"approaches":[115],"finding":[117],"solutions,":[120],"including":[121],"homotopy":[122],"continuation":[123],"methods":[124,137],"and":[125,142,145],"Grobner":[126],"basis":[127],"methods.":[128],"outperforms":[134],"these":[135],"other":[136],"low-,":[140],"medium-,":[141],"high-degree":[143],"settings":[144],"scales":[146],"better":[147],"with":[148],"buses.":[152]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}