{"id":"https://openalex.org/W2169097015","doi":"https://doi.org/10.1142/s0218195995000155","title":"COMPUTING THE ALL-PAIRS LONGEST CHAINS IN THE PLANE","display_name":"COMPUTING THE ALL-PAIRS LONGEST CHAINS IN THE PLANE","publication_year":1995,"publication_date":"1995-09-01","ids":{"openalex":"https://openalex.org/W2169097015","doi":"https://doi.org/10.1142/s0218195995000155","mag":"2169097015"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195995000155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195995000155","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","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/A5113562454","display_name":"Mikhail J. Atallah","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"MIKHAIL J. ATALLAH","raw_affiliation_strings":["Department of Computer Sciences, Purdue University, West Lafayette, Indiana 47907, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Sciences, Purdue University, West Lafayette, Indiana 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060901632","display_name":"Danny Z. Chen","orcid":"https://orcid.org/0000-0001-6565-2884"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"DANNY Z. CHEN","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113562454"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":0.521,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68645771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"05","issue":"03","first_page":"257","last_page":"271"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.7146373391151428},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.6575281023979187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5773033499717712},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5617128610610962},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5158423781394958},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5000150203704834},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4939144253730774},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4843810498714447},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.47306549549102783},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45710429549217224},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.42238855361938477},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.412592351436615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39854633808135986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3118647038936615},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3096351623535156}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7146373391151428},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6575281023979187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5773033499717712},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5617128610610962},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5158423781394958},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5000150203704834},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4939144253730774},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4843810498714447},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47306549549102783},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45710429549217224},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.42238855361938477},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.412592351436615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39854633808135986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3118647038936615},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3096351623535156},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195995000155","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195995000155","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","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":17,"referenced_works":["https://openalex.org/W11969735","https://openalex.org/W109407819","https://openalex.org/W1995040285","https://openalex.org/W2008836603","https://openalex.org/W2022971294","https://openalex.org/W2024244897","https://openalex.org/W2025641440","https://openalex.org/W2031911173","https://openalex.org/W2033520777","https://openalex.org/W2048237851","https://openalex.org/W2049520215","https://openalex.org/W2052850644","https://openalex.org/W2069893028","https://openalex.org/W2076009323","https://openalex.org/W2096827683","https://openalex.org/W2125837271","https://openalex.org/W2130566259"],"related_works":["https://openalex.org/W4377371889","https://openalex.org/W4389362338","https://openalex.org/W2113623403","https://openalex.org/W2055932080","https://openalex.org/W1968512104","https://openalex.org/W2565109825","https://openalex.org/W1862126075","https://openalex.org/W2055625272","https://openalex.org/W2036758175","https://openalex.org/W78560857"],"abstract_inverted_index":{"Many":[0],"problems":[1],"on":[2,5,156],"sequences":[3],"and":[4,50,81,139],"special":[6],"kinds":[7],"of":[8,13,25,35,39,46,53,125,152,154,162],"graphs":[9],"involve":[10],"the":[11,19,29,33,37,51,58,110,123,140,150,163],"computation":[12],"longest":[14,40,60,127],"chains":[15],"passing":[16],"points":[17,27,47,132,153],"in":[18,28,48,76,97,109,120,133],"plane.":[20],"Given":[21],"a":[22,65,88,126],"set":[23],"S":[24,134,155],"n":[26,59],"plane,":[30],"we":[31],"consider":[32],"problem":[34],"computing":[36,70],"matrix":[38,52],"chain":[41,61,128,142],"lengths":[42],"between":[43,129],"all":[44],"pairs":[45],"S,":[49],"\u201cparent\u201d":[54],"pointers":[55],"that":[56,93,157],"describes":[57],"trees.":[62],"We":[63,85],"present":[64,87],"simple":[66],"sequential":[67],"algorithm":[68,74,92],"for":[69],"these":[71,95],"matrices.":[72],"Our":[73],"runs":[75],"O(n":[77,104,166],"2":[78,100,105,167],")":[79,101],"time,":[80,122],"hence":[82],"is":[83,149,165],"optimal.":[84],"also":[86],"rather":[89],"involved":[90],"parallel":[91],"computes":[94],"matrices":[96,115],"O((log":[98],"n)":[99,107],"time":[102],"using":[103,136,144],"/log":[106],"processors":[108],"CREW":[111],"PRAM":[112],"model.":[113],"These":[114],"enable":[116],"us":[117],"to":[118],"report,":[119],"O(1)":[121],"length":[124],"any":[130],"two":[131],"by":[135,143],"one":[137],"processor,":[138],"actual":[141],"k":[145,148],"processors,":[146],"where":[147],"number":[151],"chain.":[158],"The":[159],"space":[160],"complexity":[161],"algorithms":[164],").":[168]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}