{"id":"https://openalex.org/W2152356197","doi":"https://doi.org/10.1002/rsa.3240070202","title":"Bounded branching process and and/or tree evaluation","display_name":"Bounded branching process and and/or tree evaluation","publication_year":1995,"publication_date":"1995-09-01","ids":{"openalex":"https://openalex.org/W2152356197","doi":"https://doi.org/10.1002/rsa.3240070202","mag":"2152356197"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240070202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240070202","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","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/A5068875104","display_name":"Richard M. Karp","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]},{"id":"https://openalex.org/I1297971548","display_name":"International Computer Science Institute","ror":"https://ror.org/01ewh7m12","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1297971548"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard M. Karp","raw_affiliation_strings":["Computer Science Division, University of California, Berkeley, CA 94720 and International Computer Science Institute, Berkeley, CA 94704"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, University of California, Berkeley, CA 94720 and International Computer Science Institute, Berkeley, CA 94704","institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114888990","display_name":"Yanjun Zhang","orcid":"https://orcid.org/0009-0003-1305-9626"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yanjun Zhang","raw_affiliation_strings":["Department of Computer Science and Engineering, Southern Methodist University, Dallas, TX 75275"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Southern Methodist University, Dallas, TX 75275","institution_ids":["https://openalex.org/I178169726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068875104"],"corresponding_institution_ids":["https://openalex.org/I1297971548","https://openalex.org/I95457486"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":1.7668,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.84222693,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"97","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.8640114068984985},{"id":"https://openalex.org/keywords/branching-process","display_name":"Branching process","score":0.7382356524467468},{"id":"https://openalex.org/keywords/branching","display_name":"Branching (polymer chemistry)","score":0.6728235483169556},{"id":"https://openalex.org/keywords/supercritical-fluid","display_name":"Supercritical fluid","score":0.5654210448265076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5516246557235718},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5287363529205322},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5155053734779358},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5092031359672546},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4463408291339874},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4297899603843689},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2105061113834381},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13860496878623962},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13012537360191345},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07915642857551575}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8640114068984985},{"id":"https://openalex.org/C177255742","wikidata":"https://www.wikidata.org/wiki/Q4109953","display_name":"Branching process","level":2,"score":0.7382356524467468},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.6728235483169556},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.5654210448265076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5516246557235718},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5287363529205322},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5155053734779358},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5092031359672546},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4463408291339874},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4297899603843689},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2105061113834381},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13860496878623962},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13012537360191345},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07915642857551575},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/rsa.3240070202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240070202","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures & Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W800068494","https://openalex.org/W1574558330","https://openalex.org/W1965399019","https://openalex.org/W1981139557","https://openalex.org/W1987842530","https://openalex.org/W2042231724","https://openalex.org/W2047967720","https://openalex.org/W2053172003","https://openalex.org/W2084077236","https://openalex.org/W2090441410","https://openalex.org/W2103012681","https://openalex.org/W2123540893","https://openalex.org/W2493844837","https://openalex.org/W4233413206","https://openalex.org/W4244638572","https://openalex.org/W4250057331","https://openalex.org/W4297962570"],"related_works":["https://openalex.org/W3196163622","https://openalex.org/W2370685986","https://openalex.org/W4388805554","https://openalex.org/W2371292460","https://openalex.org/W2040168466","https://openalex.org/W2130313128","https://openalex.org/W7632529","https://openalex.org/W2382967792","https://openalex.org/W2030362416","https://openalex.org/W3182923139"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"the":[3,12,47,63,74,90,120,138,142],"tail":[4],"distribution":[5],"of":[6,14,16,92,123,137],"supercritical":[7,23,111],"branching":[8,24,112],"processes":[9],"for":[10,96],"which":[11],"number":[13],"offspring":[15,33],"an":[17,85],"element":[18,78],"is":[19,126],"bounded.":[20],"Given":[21],"a":[22,31,37,59,93,109,134],"process":[25,113],"{":[26],"Z":[27,50,55,66],"n":[28,51,56,67,70],"}":[29],"with":[30,114,133],"bounded":[32,115],"distribution,":[34],"we":[35,87],"derive":[36],"tight":[38],"bound,":[39],"decaying":[40],"super\u2010exponentially":[41],"fast":[42],"as":[43,108,141],"c":[44],"increases,":[45],"on":[46,62],"probability":[48,64],"Pr[":[49,65],">":[52],"cE":[53],"(":[54],")],":[57],"and":[58,117],"similar":[60],"bound":[61],"\u2264":[68],"E(Z":[69],")/c":[71],"]":[72],"under":[73],"assumption":[75],"that":[76,89,119],"each":[77],"generates":[79],"at":[80],"least":[81],"two":[82],"offspring.":[83],"As":[84],"application,":[86],"observe":[88],"execution":[91,121],"canonical":[94],"algorithm":[95,125],"evaluating":[97],"uniform":[98],"AND/OR":[99],"trees":[100],"in":[101],"certain":[102],"probabilistic":[103],"models":[104],"can":[105],"be":[106],"viewed":[107],"two\u2010type":[110],"offspring,":[116],"show":[118],"time":[122],"this":[124],"likely":[127],"to":[128],"concentrate":[129],"around":[130],"its":[131],"expectation,":[132],"standard":[135],"deviation":[136],"same":[139],"order":[140],"expectation.":[143]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}