{"id":"https://openalex.org/W2042508971","doi":"https://doi.org/10.1137/0209052","title":"Compatible Orderings on the Metric Theory of Trees","display_name":"Compatible Orderings on the Metric Theory of Trees","publication_year":1980,"publication_date":"1980-11-01","ids":{"openalex":"https://openalex.org/W2042508971","doi":"https://doi.org/10.1137/0209052","mag":"2042508971"},"language":"en","primary_location":{"id":"doi:10.1137/0209052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209052","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5050710436","display_name":"Stephen L. Bloom","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stephen L. Bloom","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5051837370","display_name":"Ralph Tindell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ralph Tindell","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050710436"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3715,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.95100474,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"4","first_page":"683","last_page":"691"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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/T12002","display_name":"Computability, Logic, AI Algorithms","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/T11567","display_name":"semigroups and automata theory","score":0.9994999766349792,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.998199999332428,"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/combinatorics","display_name":"Combinatorics","score":0.6995026469230652},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6720282435417175},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5605827569961548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5585358142852783},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4939160943031311},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4618052840232849},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.4308314919471741},{"id":"https://openalex.org/keywords/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.4165078401565552},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3782951235771179},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.26691263914108276},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.25959259271621704},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1436644196510315},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.12458693981170654},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.08005544543266296}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6995026469230652},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6720282435417175},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5605827569961548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5585358142852783},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4939160943031311},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4618052840232849},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.4308314919471741},{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.4165078401565552},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3782951235771179},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.26691263914108276},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.25959259271621704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1436644196510315},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.12458693981170654},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.08005544543266296},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0209052","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0209052","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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":8,"referenced_works":["https://openalex.org/W1973187217","https://openalex.org/W1979473531","https://openalex.org/W2016972771","https://openalex.org/W2082477520","https://openalex.org/W2107674601","https://openalex.org/W4210249530","https://openalex.org/W4232114544","https://openalex.org/W4240176614"],"related_works":["https://openalex.org/W2042273420","https://openalex.org/W2005450316","https://openalex.org/W2090953203","https://openalex.org/W2159161388","https://openalex.org/W2010333092","https://openalex.org/W2092070151","https://openalex.org/W1988771411","https://openalex.org/W4287754152","https://openalex.org/W3036355309","https://openalex.org/W1998007190"],"abstract_inverted_index":{"In":[0],"many":[1],"studies":[2],"of":[3,8,81,98],"computation":[4],"which":[5],"make":[6],"use":[7],"rooted":[9],"labeled":[10,47,83],"trees":[11,20,78,114,127],"a":[12,45,62,122],"partial":[13,123,139],"ordering":[14,124,140],"is":[15,33,44,55,95],"usually":[16],"imposed":[17],"on":[18,125],"the":[19,22,38,91,96,99,126,129,138,143],"in":[21,105,128],"following":[23,92],"way.":[24],"A":[25,52,64],"particular":[26],"label,":[27],"say":[28],"$":[29,48,84,101,104,115,117,146],"\\bot":[30,49,85,102,116,147],"_0":[31,50,86,103,148],"$,":[32],"distinguished":[34],"and":[35,111],"identified":[36],"with":[37],"atomic":[39,144],"tree":[40,53,63,65,100,145],"whose":[41],"only":[42],"vertex":[43],"leaf":[46],"$.":[51,87],"f":[54,73,82],"then":[56],"defined":[57,141],"to":[58,79,120],"be":[59,70,118],"less":[60],"than":[61],"g":[66,68],"if":[67,135],"can":[69],"obtained":[71],"from":[72],"by":[74],"attaching":[75],"some":[76],"new":[77],"leaves":[80],"This":[88],"paper":[89],"answers":[90],"questions.":[93],"What":[94],"significance":[97],"this":[106],"ordering?":[107],"Can":[108],"other":[109],"nonatomic":[110],"perhaps":[112],"infinite":[113],"used":[119],"define":[121],"same":[130],"way?":[131],"If":[132],"so,":[133],"what":[134],"anything":[136],"distinguishes":[137],"via":[142],"$?":[149]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
