{"id":"https://openalex.org/W4307561207","doi":"https://doi.org/10.1155/2022/9954014","title":"Reach\u2010Avoid Games with a Time Limit and Detection Range: A Geometric Approach","display_name":"Reach\u2010Avoid Games with a Time Limit and Detection Range: A Geometric Approach","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4307561207","doi":"https://doi.org/10.1155/2022/9954014"},"language":"en","primary_location":{"id":"doi:10.1155/2022/9954014","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/9954014","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/9954014.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2022/9954014.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101651497","display_name":"Xi Chen","orcid":"https://orcid.org/0000-0002-8355-8952"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210122323","display_name":"Aerospace Technology Institute","ror":"https://ror.org/030n6z794","country_code":"GB","type":"other","lineage":["https://openalex.org/I4210122323"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Xi Chen","raw_affiliation_strings":["Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081"],"raw_orcid":"https://orcid.org/0000-0002-8355-8952","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081","institution_ids":["https://openalex.org/I4210122323","https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103128003","display_name":"Jianqiao Yu","orcid":"https://orcid.org/0000-0001-9352-9250"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210122323","display_name":"Aerospace Technology Institute","ror":"https://ror.org/030n6z794","country_code":"GB","type":"other","lineage":["https://openalex.org/I4210122323"]}],"countries":["CN","GB"],"is_corresponding":true,"raw_author_name":"Jianqiao Yu","raw_affiliation_strings":["Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081"],"raw_orcid":"https://orcid.org/0000-0001-9352-9250","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081","institution_ids":["https://openalex.org/I4210122323","https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045595638","display_name":"Kang Niu","orcid":"https://orcid.org/0000-0001-7688-9043"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210122323","display_name":"Aerospace Technology Institute","ror":"https://ror.org/030n6z794","country_code":"GB","type":"other","lineage":["https://openalex.org/I4210122323"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Kang Niu","raw_affiliation_strings":["Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081"],"raw_orcid":"https://orcid.org/0000-0001-7688-9043","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081","institution_ids":["https://openalex.org/I4210122323","https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066377318","display_name":"Di Yang","orcid":"https://orcid.org/0000-0001-6074-873X"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210122323","display_name":"Aerospace Technology Institute","ror":"https://ror.org/030n6z794","country_code":"GB","type":"other","lineage":["https://openalex.org/I4210122323"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Di Yang","raw_affiliation_strings":["Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081"],"raw_orcid":"https://orcid.org/0000-0001-6074-873X","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081","institution_ids":["https://openalex.org/I4210122323","https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068082800","display_name":"Jiaxun Li","orcid":"https://orcid.org/0000-0002-8831-7330"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210122323","display_name":"Aerospace Technology Institute","ror":"https://ror.org/030n6z794","country_code":"GB","type":"other","lineage":["https://openalex.org/I4210122323"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Jiaxun Li","raw_affiliation_strings":["Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081"],"raw_orcid":"https://orcid.org/0000-0002-8831-7330","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081","institution_ids":["https://openalex.org/I4210122323","https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5103128003"],"corresponding_institution_ids":["https://openalex.org/I125839683","https://openalex.org/I4210122323"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18948616,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T13371","display_name":"Military Defense Systems Analysis","score":0.9607999920845032,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11574","display_name":"Artificial Intelligence in Games","score":0.9510999917984009,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7573834657669067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.719580888748169},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6513022184371948},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6050376892089844},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5812480449676514},{"id":"https://openalex.org/keywords/time-limit","display_name":"Time limit","score":0.5445618033409119},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5157797336578369},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.45373693108558655},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4223783016204834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35355764627456665},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.29557710886001587},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.260819673538208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20609495043754578}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7573834657669067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.719580888748169},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6513022184371948},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6050376892089844},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5812480449676514},{"id":"https://openalex.org/C2781011336","wikidata":"https://www.wikidata.org/wiki/Q1465133","display_name":"Time limit","level":2,"score":0.5445618033409119},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5157797336578369},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.45373693108558655},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4223783016204834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35355764627456665},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.29557710886001587},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.260819673538208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20609495043754578},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/9954014","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/9954014","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/9954014.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:9954014","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/9954014.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:9d0dd15bc88d4b29830198b4d4b0411c","is_oa":true,"landing_page_url":"https://doaj.org/article/9d0dd15bc88d4b29830198b4d4b0411c","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/9954014","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/9954014","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/9954014.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307561207.pdf","grobid_xml":"https://content.openalex.org/works/W4307561207.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W2009318488","https://openalex.org/W2010674941","https://openalex.org/W2016181942","https://openalex.org/W2071766053","https://openalex.org/W2106816694","https://openalex.org/W2183469038","https://openalex.org/W2288883172","https://openalex.org/W2414457428","https://openalex.org/W2498529546","https://openalex.org/W2507881886","https://openalex.org/W2735367601","https://openalex.org/W2745616146","https://openalex.org/W2765787247","https://openalex.org/W2766538102","https://openalex.org/W2771197443","https://openalex.org/W2772402455","https://openalex.org/W2785598896","https://openalex.org/W2791080580","https://openalex.org/W2898083769","https://openalex.org/W2911234349","https://openalex.org/W2911675879","https://openalex.org/W2913295839","https://openalex.org/W2946040522","https://openalex.org/W2972260985","https://openalex.org/W2990482634","https://openalex.org/W2994078358","https://openalex.org/W3001813235","https://openalex.org/W3006248364","https://openalex.org/W3017102765","https://openalex.org/W3021733985","https://openalex.org/W3024030038","https://openalex.org/W3127927628","https://openalex.org/W3201312234","https://openalex.org/W3215236701","https://openalex.org/W4205317374"],"related_works":["https://openalex.org/W2087914290","https://openalex.org/W2945274325","https://openalex.org/W2375762310","https://openalex.org/W1225023418","https://openalex.org/W2367766247","https://openalex.org/W2363664274","https://openalex.org/W2379345400","https://openalex.org/W2350086347","https://openalex.org/W2361702302","https://openalex.org/W4285111597"],"abstract_inverted_index":{"The":[0,59,75,177],"reach\u2010avoid":[1],"game":[2,98,153,201,212],"theory":[3],"is":[4,88,93,123,141,163],"an":[5],"ideal":[6],"tool":[7],"to":[8,46,56,62,80,95,191],"handle":[9],"the":[10,29,32,40,44,48,57,64,82,86,102,106,110,115,118,121,127,136,144,152,161,167,171,175,188,193,200,207,211],"conflicts":[11],"among":[12],"intelligent":[13],"agents":[14],"and":[15,24,50,109,126,170,204],"has":[16],"been":[17],"previously":[18],"studied":[19],"assuming":[20],"full":[21],"state":[22],"information":[23],"no":[25],"time":[26,54,73,172],"limits":[27],"on":[28,166],"players":[30,162],"in":[31,213],"past":[33],"decades.":[34],"In":[35],"this":[36,97,181,185],"article,":[37],"we":[38,113,205],"extend":[39],"problem":[41],"by":[42],"requiring":[43],"defender":[45,76],"detect":[47],"attacker":[49,60,83,87,122],"adding":[51],"maximum":[52],"operation":[53],"constraints":[55],"attacker.":[58,176],"aims":[61],"reach":[63],"target":[65,137],"region":[66,138],"without":[67],"being":[68],"captured":[69],"or":[70],"reaching":[71],"its":[72,133],"limit.":[74],"can":[77],"employ":[78],"strategies":[79],"intercept":[81],"only":[84],"when":[85,139],"detected.":[89],"A":[90],"geometric":[91,103],"method":[92],"proposed":[94],"solve":[96],"qualitatively.":[99],"By":[100],"analyzing":[101],"property":[104],"of":[105,160,174,180,210],"Apollonian":[107],"circle":[108],"detection":[111,145],"range,":[112],"give":[114],"barrier":[116,149],"under":[117],"condition":[119],"that":[120,150,184],"initially":[124,142],"detected":[125],"attacker\u2019s":[128],"shortest":[129,168],"route":[130,169],"which":[131,198],"guarantees":[132],"arrival":[134],"at":[135],"it":[140],"outside":[143],"range.":[146],"Then,":[147],"a":[148],"separates":[151],"space":[154],"into":[155],"two":[156,195],"respective":[157],"winning":[158],"regions":[159],"constructed":[164],"based":[165],"limit":[173],"main":[178],"contributions":[179],"work":[182],"are":[183],"paper":[186],"provides":[187],"first":[189],"attempt":[190],"introduce":[192],"abovementioned":[194],"concepts":[196],"simultaneously,":[197],"makes":[199],"more":[202],"practical,":[203],"provide":[206],"complete":[208],"solution":[209],"all":[214],"possible":[215],"situations.":[216]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}