{"id":"https://openalex.org/W4413375471","doi":"https://doi.org/10.1007/s44443-025-00227-8","title":"Multi-layer obstacle-avoiding rectilinear steiner minimal tree algorithm based on deep reinforcement learning","display_name":"Multi-layer obstacle-avoiding rectilinear steiner minimal tree algorithm based on deep reinforcement learning","publication_year":2025,"publication_date":"2025-08-21","ids":{"openalex":"https://openalex.org/W4413375471","doi":"https://doi.org/10.1007/s44443-025-00227-8"},"language":"en","primary_location":{"id":"doi:10.1007/s44443-025-00227-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44443-025-00227-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44443-025-00227-8.pdf","source":{"id":"https://openalex.org/S2764955546","display_name":"Journal of King Saud University - Computer and Information Sciences","issn_l":"1319-1578","issn":["1319-1578","2213-1248"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University Computer and Information Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s44443-025-00227-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017381514","display_name":"Xing Huang","orcid":"https://orcid.org/0000-0002-5396-110X"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xing Huang","raw_affiliation_strings":["School of Big Data, Fuzhou University of International Studies and Trade, No.28, Yuhuan Road, 350202, Fuzhou, Fujian, China","School of Computer Science, Northwestern Polytechnical University, No.127, Youyi West Road, 710072, Xi\u2019an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Big Data, Fuzhou University of International Studies and Trade, No.28, Yuhuan Road, 350202, Fuzhou, Fujian, China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"School of Computer Science, Northwestern Polytechnical University, No.127, Youyi West Road, 710072, Xi\u2019an, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089098757","display_name":"Yuhan Zhu","orcid":"https://orcid.org/0000-0002-0246-3653"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuhan Zhu","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014538929","display_name":"Yanbo Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanbo Xu","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101988547","display_name":"Yajun Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yajun Xie","raw_affiliation_strings":["School of Big Data, Fuzhou University of International Studies and Trade, No.28, Yuhuan Road, 350202, Fuzhou, Fujian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Big Data, Fuzhou University of International Studies and Trade, No.28, Yuhuan Road, 350202, Fuzhou, Fujian, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045753829","display_name":"Genggeng Liu","orcid":"https://orcid.org/0000-0002-3099-4371"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Genggeng Liu","raw_affiliation_strings":["College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China"],"raw_orcid":"https://orcid.org/0000-0002-3099-4371","affiliations":[{"raw_affiliation_string":"College of Computer and Data Science, Fuzhou University, No.2, Xueyuan Road, 350108, Fuzhou, Fujian, China","institution_ids":["https://openalex.org/I80947539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045753829"],"corresponding_institution_ids":["https://openalex.org/I80947539"],"apc_list":{"value":1350,"currency":"USD","value_usd":1350},"apc_paid":{"value":1350,"currency":"USD","value_usd":1350},"fwci":0.4626,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66503222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"37","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9968000054359436,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9968000054359436,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9599000215530396,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9314000010490417,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.8758442401885986},{"id":"https://openalex.org/keywords/obstacle","display_name":"Obstacle","score":0.6590244174003601},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6222403049468994},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5539195537567139},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5133156180381775},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.474230021238327},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.442543089389801},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3899264931678772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3062933683395386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25479769706726074},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08874055743217468},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.04646259546279907},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.046421825885772705}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.8758442401885986},{"id":"https://openalex.org/C2776650193","wikidata":"https://www.wikidata.org/wiki/Q264661","display_name":"Obstacle","level":2,"score":0.6590244174003601},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6222403049468994},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5539195537567139},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5133156180381775},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.474230021238327},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.442543089389801},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3899264931678772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3062933683395386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25479769706726074},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08874055743217468},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.04646259546279907},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.046421825885772705},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s44443-025-00227-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44443-025-00227-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44443-025-00227-8.pdf","source":{"id":"https://openalex.org/S2764955546","display_name":"Journal of King Saud University - Computer and Information Sciences","issn_l":"1319-1578","issn":["1319-1578","2213-1248"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University Computer and Information Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c1d12af3abad48deae0578144e0ceec3","is_oa":true,"landing_page_url":"https://doaj.org/article/c1d12af3abad48deae0578144e0ceec3","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":"Journal of King Saud University: Computer and Information Sciences, Vol 37, Iss 7, Pp 1-20 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s44443-025-00227-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s44443-025-00227-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s44443-025-00227-8.pdf","source":{"id":"https://openalex.org/S2764955546","display_name":"Journal of King Saud University - Computer and Information Sciences","issn_l":"1319-1578","issn":["1319-1578","2213-1248"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of King Saud University Computer and Information Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3949464299","display_name":null,"funder_award_id":"62372109","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7763609805","display_name":null,"funder_award_id":"62372109","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"},{"id":"https://openalex.org/G8086747769","display_name":"\u5fae\u6d41\u63a7FPVA\u751f\u7269\u82af\u7247\u6d4b\u8bd5\u81ea\u52a8\u5316\u65b9\u6cd5\u7814\u7a76","funder_award_id":"2024J01984","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413375471.pdf","grobid_xml":"https://content.openalex.org/works/W4413375471.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W251392994","https://openalex.org/W1944814515","https://openalex.org/W1979832172","https://openalex.org/W2020112047","https://openalex.org/W2025658531","https://openalex.org/W2035622528","https://openalex.org/W2037342223","https://openalex.org/W2065255302","https://openalex.org/W2069712919","https://openalex.org/W2117449332","https://openalex.org/W2118320476","https://openalex.org/W2142927985","https://openalex.org/W2156154019","https://openalex.org/W2159505989","https://openalex.org/W2160642395","https://openalex.org/W2162320001","https://openalex.org/W2802244581","https://openalex.org/W2980548235","https://openalex.org/W3211880575","https://openalex.org/W3216031235","https://openalex.org/W4223962722","https://openalex.org/W4226286144","https://openalex.org/W4232025991","https://openalex.org/W4232765531","https://openalex.org/W4318769170","https://openalex.org/W4372046852","https://openalex.org/W4386269701","https://openalex.org/W4391341394","https://openalex.org/W4392679179","https://openalex.org/W4392858312","https://openalex.org/W4395695599","https://openalex.org/W4396812335","https://openalex.org/W4399881351","https://openalex.org/W4404133993","https://openalex.org/W4404134172","https://openalex.org/W4405846157","https://openalex.org/W4409362798"],"related_works":["https://openalex.org/W2118320476","https://openalex.org/W2161182859","https://openalex.org/W2025658531","https://openalex.org/W2794103424","https://openalex.org/W1503036335","https://openalex.org/W4244816249","https://openalex.org/W2115973883","https://openalex.org/W2739242419","https://openalex.org/W1996530509","https://openalex.org/W2054452185"],"abstract_inverted_index":{"As":[0],"chip":[1,20],"interconnect":[2,40],"density":[3],"increases,":[4],"routing":[5,11,122,190],"problems":[6],"become":[7],"increasingly":[8],"complex.":[9],"The":[10],"scheme":[12],"significantly":[13],"impacts":[14],"key":[15],"performance":[16],"indicators":[17],"such":[18],"as":[19],"delay,":[21],"power":[22],"consumption,":[23],"and":[24,66,161],"area.":[25],"In":[26],"Very":[27],"Large-Scale":[28],"Integration":[29],"(VLSI)":[30],"routing,":[31,52],"the":[32,70,119,135,155,168,185],"rectilinear":[33],"Steiner":[34,74,138],"minimal":[35],"tree":[36],"is":[37,107,127,150],"an":[38,92,125,181],"excellent":[39],"model":[41],"for":[42,133],"multi-pin":[43],"nets.":[44],"However,":[45],"modern":[46],"VLSI":[47,82],"designs":[48],"require":[49],"multi-layer":[50,103,120],"obstacle-avoiding":[51,104,121],"where":[53],"wires":[54],"must":[55],"traverse":[56],"multiple":[57],"metal":[58],"layers":[59,116],"while":[60],"avoiding":[61],"obstacles":[62],"to":[63,117,129,152,176],"ensure":[64],"connectivity":[65],"performance.":[67],"This":[68],"makes":[69],"Multi-Layer":[71,136],"Obstacle-Avoiding":[72,137],"Rectilinear":[73],"Minimal":[75],"Tree":[76,139],"(ML-OARSMT)":[77],"problem":[78],"highly":[79],"challenging":[80],"in":[81,189],"physical":[83],"design.":[84],"To":[85],"address":[86],"this":[87,89],"issue,":[88],"paper":[90],"proposes":[91],"ML-OARSMT":[93],"construction":[94],"algorithm":[95,170],"based":[96],"on":[97],"deep":[98],"reinforcement":[99],"learning.":[100],"First,":[101],"a":[102,147],"spanning":[105],"graph":[106],"constructed":[108],"by":[109],"introducing":[110],"vertex":[111],"mapping,":[112],"which":[113],"connects":[114],"different":[115],"handle":[118],"problem.":[123],"Then,":[124],"agent":[126],"designed":[128],"learn":[130],"edge":[131],"selection":[132],"constructing":[134],"(ML-OAST)":[140],"using":[141],"Double":[142],"Deep":[143],"Q-Network":[144],"(DDQN).":[145],"Finally,":[146],"post-processing":[148],"stage":[149],"applied":[151],"further":[153],"shorten":[154],"total":[156],"wirelength":[157,173],"through":[158],"fast":[159],"pruning":[160],"local":[162],"optimization.":[163,191],"Experimental":[164],"results":[165],"demonstrate":[166],"that":[167],"proposed":[169],"achieves":[171],"better":[172],"quality":[174],"compared":[175],"state-of-the-art":[177],"heuristic":[178],"algorithms.":[179],"Additionally,":[180],"ablation":[182],"study":[183],"confirms":[184],"effectiveness":[186],"of":[187],"DDQN":[188]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}
