{"id":"https://openalex.org/W2570242489","doi":"https://doi.org/10.1080/10556788.2015.1130130","title":"An approximation algorithm for the longest path problem in solid grid graphs","display_name":"An approximation algorithm for the longest path problem in solid grid graphs","publication_year":2016,"publication_date":"2016-01-12","ids":{"openalex":"https://openalex.org/W2570242489","doi":"https://doi.org/10.1080/10556788.2015.1130130","mag":"2570242489"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2015.1130130","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1130130","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5023348511","display_name":"Asghar Asgharian Sardroud","orcid":"https://orcid.org/0000-0003-0644-940X"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Asghar Asgharian Sardroud","raw_affiliation_strings":["Department of Computer Engineering and IT, Amirkabir University of Technology, Tehran, Iran","Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and IT, Amirkabir University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran#TAB#","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074487575","display_name":"Alireza Bagheri","orcid":"https://orcid.org/0000-0002-3542-7763"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Alireza Bagheri","raw_affiliation_strings":["Department of Computer Engineering and IT, Amirkabir University of Technology, Tehran, Iran","Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and IT, Amirkabir University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I158248296"]},{"raw_affiliation_string":"Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran#TAB#","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074487575"],"corresponding_institution_ids":["https://openalex.org/I158248296"],"apc_list":null,"apc_paid":null,"fwci":1.0454,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81096397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"3","first_page":"479","last_page":"493"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T12541","display_name":"Graph Labeling and Dimension Problems","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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/grid","display_name":"Grid","score":0.5564841032028198},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5457444190979004},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5176616311073303},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.5175437331199646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49607643485069275},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36240512132644653},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3579965829849243},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.28939151763916016},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.2814220190048218},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2040417194366455},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05427953600883484}],"concepts":[{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5564841032028198},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5457444190979004},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5176616311073303},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.5175437331199646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49607643485069275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36240512132644653},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3579965829849243},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28939151763916016},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.2814220190048218},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2040417194366455},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05427953600883484},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2015.1130130","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1130130","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1122825014","display_name":null,"funder_award_id":"40/532","funder_id":"https://openalex.org/F4320321431","funder_display_name":"Amirkabir University of Technology"}],"funders":[{"id":"https://openalex.org/F4320321431","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W411619626","https://openalex.org/W1548700236","https://openalex.org/W1555471913","https://openalex.org/W1580484824","https://openalex.org/W1708444016","https://openalex.org/W1813313303","https://openalex.org/W1885568428","https://openalex.org/W1967041330","https://openalex.org/W1976157781","https://openalex.org/W1985773538","https://openalex.org/W1993042687","https://openalex.org/W2023908757","https://openalex.org/W2033829723","https://openalex.org/W2045021308","https://openalex.org/W2046496468","https://openalex.org/W2047176418","https://openalex.org/W2047690551","https://openalex.org/W2055336889","https://openalex.org/W2056724312","https://openalex.org/W2058198905","https://openalex.org/W2058687965","https://openalex.org/W2083537714","https://openalex.org/W2162053220","https://openalex.org/W2169444479","https://openalex.org/W2296148711","https://openalex.org/W2962700727","https://openalex.org/W4240930434"],"related_works":["https://openalex.org/W2132921321","https://openalex.org/W2065006817","https://openalex.org/W2129550502","https://openalex.org/W2116465486","https://openalex.org/W2101572961","https://openalex.org/W1995629993","https://openalex.org/W1759713541","https://openalex.org/W2551933747","https://openalex.org/W2045633099","https://openalex.org/W2135694842"],"abstract_inverted_index":{"The":[0],"longest":[1,63,76],"path":[2,64,77],"problem":[3,8,31,43,65],"is":[4,44],"a":[5,23,57,85],"well-known":[6],"NP-hard":[7],"which":[9,29],"can":[10,32,72],"be":[11,33],"used":[12],"to":[13,46],"model":[14],"and":[15],"solve":[16],"some":[17],"optimization":[18],"problems.":[19],"There":[20],"are":[21],"only":[22],"few":[24],"classes":[25],"of":[26,84],"graphs":[27],"for":[28,52,61],"this":[30],"solved":[34],"polynomially.":[35],"In":[36],"addition,":[37],"the":[38,42,62,75,90],"results":[39],"show":[40],"that":[41],"hard":[45],"approximate":[47,74],"within":[48,89],"any":[49,79],"reasonable":[50],"factor":[51],"general":[53],"graphs.":[54,69],"We":[55],"introduce":[56],"polynomial-time":[58],"-approximation":[59],"algorithm":[60,71],"in":[66],"solid":[67,86],"grid":[68,87],"Our":[70],"also":[73],"between":[78],"two":[80],"given":[81],"boundary":[82],"vertices":[83],"graph":[88],"same":[91],"approximation":[92],"factor.":[93]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}