{"id":"https://openalex.org/W2809001843","doi":"https://doi.org/10.1145/3210377.3210387","title":"Red-Blue Pebble Game","display_name":"Red-Blue Pebble Game","publication_year":2018,"publication_date":"2018-07-11","ids":{"openalex":"https://openalex.org/W2809001843","doi":"https://doi.org/10.1145/3210377.3210387","mag":"2809001843"},"language":"en","primary_location":{"id":"doi:10.1145/3210377.3210387","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210387","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210387","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210387","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083684609","display_name":"Erik D. Demaine","orcid":"https://orcid.org/0000-0003-3803-5703"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erik D. Demaine","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070332039","display_name":"Quanquan C. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Quanquan C. Liu","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083684609"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.0687,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.79413196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"195","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.995199978351593,"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/pebble","display_name":"Pebble","score":0.8581820726394653},{"id":"https://openalex.org/keywords/cache","display_name":"Cache","score":0.753799557685852},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6904785633087158},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6077058911323547},{"id":"https://openalex.org/keywords/cache-oblivious-algorithm","display_name":"Cache-oblivious algorithm","score":0.5317336916923523},{"id":"https://openalex.org/keywords/register-allocation","display_name":"Register allocation","score":0.4389796555042267},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43886739015579224},{"id":"https://openalex.org/keywords/cache-algorithms","display_name":"Cache algorithms","score":0.4364653527736664},{"id":"https://openalex.org/keywords/cpu-cache","display_name":"CPU cache","score":0.3788553476333618},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3709866404533386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3452158570289612},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3387174606323242},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3015383780002594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23243603110313416},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.10552525520324707}],"concepts":[{"id":"https://openalex.org/C2777760186","wikidata":"https://www.wikidata.org/wiki/Q14673","display_name":"Pebble","level":2,"score":0.8581820726394653},{"id":"https://openalex.org/C115537543","wikidata":"https://www.wikidata.org/wiki/Q165596","display_name":"Cache","level":2,"score":0.753799557685852},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6904785633087158},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6077058911323547},{"id":"https://openalex.org/C59687516","wikidata":"https://www.wikidata.org/wiki/Q5015938","display_name":"Cache-oblivious algorithm","level":5,"score":0.5317336916923523},{"id":"https://openalex.org/C128916667","wikidata":"https://www.wikidata.org/wiki/Q1343660","display_name":"Register allocation","level":3,"score":0.4389796555042267},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43886739015579224},{"id":"https://openalex.org/C38556500","wikidata":"https://www.wikidata.org/wiki/Q13404475","display_name":"Cache algorithms","level":4,"score":0.4364653527736664},{"id":"https://openalex.org/C189783530","wikidata":"https://www.wikidata.org/wiki/Q352090","display_name":"CPU cache","level":3,"score":0.3788553476333618},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3709866404533386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3452158570289612},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3387174606323242},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3015383780002594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23243603110313416},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.10552525520324707},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C114793014","wikidata":"https://www.wikidata.org/wiki/Q52109","display_name":"Geomorphology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3210377.3210387","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210387","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210387","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/128439","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/128439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT web domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"}],"best_oa_location":{"id":"doi:10.1145/3210377.3210387","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3210377.3210387","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3210377.3210387","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3526151021","display_name":null,"funder_award_id":"1122374","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5635854791","display_name":null,"funder_award_id":"112237","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7297461854","display_name":null,"funder_award_id":"122374","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2809001843.pdf","grobid_xml":"https://content.openalex.org/works/W2809001843.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1972501001","https://openalex.org/W1997947415","https://openalex.org/W2011039300","https://openalex.org/W2022841964","https://openalex.org/W2036427735","https://openalex.org/W2038142281","https://openalex.org/W2056304107","https://openalex.org/W2061073612","https://openalex.org/W2061513598","https://openalex.org/W2066870457","https://openalex.org/W2070079053","https://openalex.org/W2076318470","https://openalex.org/W2188672352","https://openalex.org/W2215464783","https://openalex.org/W2461575467","https://openalex.org/W2731103471"],"related_works":["https://openalex.org/W104694020","https://openalex.org/W2480409714","https://openalex.org/W2066319772","https://openalex.org/W1908574345","https://openalex.org/W2951453665","https://openalex.org/W2556863009","https://openalex.org/W2787466783","https://openalex.org/W2782004680","https://openalex.org/W3098475836","https://openalex.org/W2006706309","https://openalex.org/W2949867448","https://openalex.org/W3124155755","https://openalex.org/W2014866763","https://openalex.org/W1984529227","https://openalex.org/W2953168049","https://openalex.org/W2007134090","https://openalex.org/W2951723302","https://openalex.org/W2613194369","https://openalex.org/W2085138698","https://openalex.org/W2025170505"],"abstract_inverted_index":{"The":[0],"red-blue":[1,34,216],"pebble":[2,35,149,217,221],"game":[3,36,144,218],"was":[4],"formulated":[5],"in":[6,57,188,284],"the":[7,11,33,127,138,147,171,201,215,240,245,265,270],"1980s~\\citeHK81":[8],"to":[9,48,107,141,219,234],"model":[10,241],"I/O":[12],"complexity":[13,172],"of":[14,84,129,161,173,184,200,204,272,291],"algorithms":[15],"on":[16,66,126,157,214],"a":[17,22,49,72,89,143,158,211,285],"two-level":[18],"memory":[19,120],"hierarchy.":[20],"Given":[21,122],"directed":[23],"acyclic":[24],"graph":[25],"representing":[26],"computations":[27],"(vertices)":[28],"and":[29,41,61,80,97,104,114,182,242],"their":[30],"dependencies":[31],"(edges),":[32],"allows":[37],"sequentially":[38],"adding,":[39],"removing,":[40],"recoloring":[42],"red":[43,53,78,90,103,130],"or":[44,109,119,223],"blue":[45,62,105],"pebbles":[46,54,63,92,98,131,156],"according":[47],"few":[50],"rules,":[51],"where":[52],"represent":[55,64],"data":[56,65,111,227],"cache":[58,136,229],"(fast":[59],"memory)":[60],"disk":[67,113],"(slow,":[68],"external":[69],"memory).":[70],"Specifically,":[71],"vertex":[73],"can":[74,93,99],"be":[75,95,100],"newly":[76],"pebbled":[77],"if":[79,82],"only":[81],"all":[83],"its":[85],"predecessors":[86],"currently":[87],"have":[88],"pebble;":[91],"always":[94],"removed;":[96],"recolored":[101],"between":[102,112,177],"(corresponding":[106],"reading":[108],"writing":[110,232],"cache,":[115],"also":[116],"called":[117],"I/Os":[118],"transfers).":[121],"an":[123,198],"upper":[124],"bound":[125],"number":[128,183,271,290],"at":[132],"any":[133],"time":[134],"(the":[135],"size),":[137],"goal":[139],"is":[140,259,274,279],"compute":[142],"execution":[145],"with":[146,155],"fewest":[148],"recolorings":[150,185],"(memory":[151,186],"transfers)":[152,187],"that":[153,254,264,277],"finish":[154],"specified":[159],"subset":[160],"nodes":[162],"(outputs":[163],"get":[164],"computed).":[165],"In":[166],"this":[167,175,194,256],"paper,":[168],"we":[169,192,209,252,262],"investigate":[170],"computing":[174],"trade-off":[176,246,266],"red-pebble":[178],"limit":[179],"(cache":[180],"size)":[181],"general":[189],"DAGs.":[190],"First":[191],"prove":[193],"problem":[195,248,267],"PSPACE-complete":[196],"through":[197],"extension":[199],"proof":[202],"PSPACE-hardness":[203],"black":[205],"pebbling":[206],"complexity~\\citeGLT80.":[207],"Second,":[208],"consider":[210],"natural":[212],"restriction":[213],"forbid":[220,225],"deletions,":[222],"equivalently,":[224],"discarding":[226],"from":[228],"without":[230],"first":[231],"it":[233],"disk.":[235],"This":[236],"assumption":[237],"both":[238],"simplifies":[239],"immediately":[243],"places":[244],"computation":[247],"within":[249],"NP.":[250],"Unfortunately,":[251],"show":[253,263],"even":[255],"restricted":[257],"version":[258],"NP-complete.":[260],"Finally,":[261],"parameterized":[268],"by":[269],"transitions":[273],"W[1]-hard,":[275],"meaning":[276],"there":[278],"likely":[280],"no":[281],"algorithm":[282],"running":[283],"fixed":[286],"polynomial":[287],"for":[288],"constant":[289],"transitions.":[292]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
