{"id":"https://openalex.org/W2064155162","doi":"https://doi.org/10.1137/070684148","title":"Memoryless Rules for Achlioptas Processes","display_name":"Memoryless Rules for Achlioptas Processes","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2064155162","doi":"https://doi.org/10.1137/070684148","mag":"2064155162"},"language":"en","primary_location":{"id":"doi:10.1137/070684148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070684148","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5073404056","display_name":"Andrew Beveridge","orcid":"https://orcid.org/0000-0002-9823-2867"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrew Beveridge","raw_affiliation_strings":["abeveridge@macalester.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"abeveridge@macalester.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079523589","display_name":"Tom Bohman","orcid":"https://orcid.org/0000-0002-4051-2401"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tom Bohman","raw_affiliation_strings":["tbohman@moser.math.cmu.edu and alan@random.math.cmu.edu and pikhurko@andrew.cmu.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"tbohman@moser.math.cmu.edu and alan@random.math.cmu.edu and pikhurko@andrew.cmu.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan Frieze","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080095759","display_name":"Oleg Pikhurko","orcid":"https://orcid.org/0000-0002-9657-4011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oleg Pikhurko","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5073404056"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8293,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68707278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"23","issue":"2","first_page":"993","last_page":"1008"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9937999844551086,"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":0.9937999844551086,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9901999831199646,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9865000247955322,"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/giant-component","display_name":"Giant component","score":0.8216379880905151},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.72365403175354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6552015542984009},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6514317393302917},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4301455020904541},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3850151300430298},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.35349512100219727},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.10397005081176758}],"concepts":[{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.8216379880905151},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.72365403175354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6552015542984009},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6514317393302917},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4301455020904541},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3850151300430298},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.35349512100219727},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.10397005081176758},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/070684148","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070684148","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.131.7924","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.7924","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~pikhurko/Papers/Memoryless.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.300.7109","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.7109","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/Texfiles/Memoryless.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.497.7524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.497.7524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.macalester.edu/~abeverid/papers/Memoryless.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7400000095367432}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W65106085","https://openalex.org/W1515742382","https://openalex.org/W1653231547","https://openalex.org/W1975999171","https://openalex.org/W2002387903","https://openalex.org/W2004427634","https://openalex.org/W2022930128","https://openalex.org/W2033468284","https://openalex.org/W2064975723","https://openalex.org/W2067951359","https://openalex.org/W2095403663","https://openalex.org/W2138359578","https://openalex.org/W2169071224","https://openalex.org/W2751862591","https://openalex.org/W2950850272","https://openalex.org/W3144881883","https://openalex.org/W4231943475","https://openalex.org/W4244198819"],"related_works":["https://openalex.org/W4293753062","https://openalex.org/W4287258775","https://openalex.org/W1889601917","https://openalex.org/W2142290020","https://openalex.org/W1965603061","https://openalex.org/W4242560956","https://openalex.org/W3137550455","https://openalex.org/W1483882171","https://openalex.org/W2950850272","https://openalex.org/W2182339161"],"abstract_inverted_index":{"In":[0],"an":[1],"Achlioptas":[2],"process":[3],"two":[4,44],"random":[5,45],"pairs":[6],"of":[7,20,81],"$\\{1,\\dots,n\\}$":[8],"arrive":[9],"in":[10,59,93],"each":[11],"round":[12],"and":[13,38,62],"the":[14,24,35,43,52,66,70,74,79,85,90,94],"player":[15,53,75],"has":[16],"to":[17,77],"choose":[18],"one":[19,40],"them.":[21],"We":[22,49],"study":[23],"very":[25],"restrictive":[26],"version":[27],"where":[28],"a":[29,56,82],"player's":[30],"decisions":[31],"cannot":[32],"depend":[33],"on":[34],"previous":[36],"history":[37],"only":[39],"vertex":[41],"from":[42],"edges":[46],"is":[47,65,88],"revealed.":[48],"prove":[50],"that":[51,63],"can":[54],"create":[55],"giant":[57],"component":[58],"$(2\\sqrt{5}-4+o(1))n=(0.4721\\ldots+o(1))n$":[60],"rounds":[61],"this":[64],"best":[67],"possible.":[68],"On":[69],"other":[71],"hand,":[72],"if":[73],"wants":[76],"delay":[78],"appearance":[80],"giant,":[83],"then":[84],"optimal":[86],"bound":[87],"$(1/2+o(1))n$,":[89],"same":[91],"as":[92],"Erd\u0151s\u2013R\u00e9nyi":[95],"model.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
