{"id":"https://openalex.org/W1980733246","doi":"https://doi.org/10.1155/1998/26574","title":"On Rectilinear Distance\u2010Preserving Trees","display_name":"On Rectilinear Distance\u2010Preserving Trees","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1980733246","doi":"https://doi.org/10.1155/1998/26574","mag":"1980733246"},"language":"en","primary_location":{"id":"doi:10.1155/1998/26574","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/26574","pdf_url":"https://downloads.hindawi.com/archive/1998/026574.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"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":"VLSI Design","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/1998/026574.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004736948","display_name":"Gustavo T\u00e8llez","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gustavo E. T\u00e9llez","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078132977","display_name":"Majid Sarrafzadeh","orcid":"https://orcid.org/0000-0001-8407-8689"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Majid Sarrafzadeh","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004736948"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":1.063,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74952793,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"1","first_page":"15","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9973999857902527,"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/algorithm","display_name":"Algorithm","score":0.6553661823272705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46297094225883484},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.323810338973999}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6553661823272705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46297094225883484},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.323810338973999}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1155/1998/26574","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/26574","pdf_url":"https://downloads.hindawi.com/archive/1998/026574.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"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":"VLSI Design","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1155/1998/26574","is_oa":true,"landing_page_url":"https://doi.org/10.1155/1998/26574","pdf_url":"https://downloads.hindawi.com/archive/1998/026574.pdf","source":{"id":"https://openalex.org/S81291924","display_name":"VLSI design","issn_l":"1026-7123","issn":["1026-7123","1065-514X","1563-5171"],"is_oa":false,"is_in_doaj":false,"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":"VLSI Design","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5438855631","display_name":null,"funder_award_id":"MIP-9207267","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6964260690","display_name":"Algorithm Design for VLSI Layout","funder_award_id":"9207267","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/W1980733246.pdf","grobid_xml":"https://content.openalex.org/works/W1980733246.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1524855799","https://openalex.org/W1578824783","https://openalex.org/W1722048720","https://openalex.org/W1940299996","https://openalex.org/W1988808425","https://openalex.org/W2005314985","https://openalex.org/W2064086982","https://openalex.org/W2069712919","https://openalex.org/W2087275089","https://openalex.org/W2141105412","https://openalex.org/W2144677702","https://openalex.org/W2156568500","https://openalex.org/W4255880171","https://openalex.org/W6634490579","https://openalex.org/W6666847974","https://openalex.org/W6667846912","https://openalex.org/W6680985272","https://openalex.org/W6681378496"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"Given":[0],"a":[1,21,26,40,123,157,278],"set":[2],"of":[3,60,112,126,186,226,229,303,331],"terminals":[4,48,304],"on":[5,233,266],"the":[6,55,58,69,85,110,115,127,154,167,187,223,227,230,240,301,324,342],"plane":[7],"N":[8,50],"=":[9],"{":[10],"s":[11,24,44],",":[12,15,25,34,45],"\u03bd":[13,17],"1":[14],"\u2026,":[16],"n":[18,135,174,180,205,220,250,254,257],"},":[19],"with":[20,132,294],"source":[22,62,74,92],"terminal":[23],"Rectilinear":[27,80,281],"Distance\u2010Preserving":[28,81],"Tree":[29,82],"(RDPT)":[30],"T":[31,203,218,252],"(":[32,134,173,179,200,204,219,249,253],"V":[33],"E":[35],")":[36,137,176,206,210,221,255,259],"is":[37,66,140,151,191,222,305],"defined":[38],"as":[39],"tree":[41,284],"rooted":[42],"at":[43],"connecting":[46],"all":[47],"in":[49,109,129,156,297,335],".":[51],"An":[52],"RDPT":[53,231,275,326],"has":[54,196,247],"property":[56],"that":[57,73,290,341],"length":[59,88],"every":[61],"to":[63,68,93,323,333],"sink":[64,94],"path":[65],"equal":[67],"rectilinear":[70],"distance":[71],"between":[72],"and":[75,162,177,271],"sink.":[76],"A":[77,118,142,184],"Min\u2010":[78],"Cost":[79,280],"(MRDPT)":[83],"minimizes":[84],"total":[86,298,336],"wire":[87],"while":[89],"maintaining":[90],"minimal":[91],"linear":[95],"delay,":[96],"making":[97],"it":[98],"suitable":[99,313],"for":[100,122,153,166,211,314],"high":[101],"performance":[102],"interconnect":[103],"applications.":[104,317],"This":[105,236,309],"paper":[106],"studies":[107],"problems":[108],"construction":[111,276],"RDPTs,":[113],"including":[114],"following":[116],"contributions.":[117],"new":[119],"exact":[120],"algorithm":[121,170,195,322,328],"restricted":[124],"version":[125],"problem":[128,155,190,232],"one":[130,234],"quadrant":[131,188,243],"O":[133,172,178,199,248],"2":[136,202,251],"time":[138,164,197,224,260],"complexity":[139,165,198,225],"proposed.":[141,192],"novel":[143],"heuristic":[144,169,274],"algorithm,":[145],"which":[146,246],"uses":[147],"optimally":[148],"solvable":[149],"sub\u2010problems,":[150],"proposed":[152,168,194,344],"single":[158],"quadrant.":[159,235],"The":[160,193],"average":[161],"worst\u2010case":[163],"are":[171,292],"3/2":[175],"3":[181,209,258],"),":[182],"respectively.":[183],"2\u2010approximation":[185],"merging":[189,244],"\u03b1":[201,208,214],"+":[207,256],"any":[212],"constant":[213],"&gt;":[215],"1,":[216],"where":[217],"solution":[228,245],"result":[237,310],"improves":[238],"over":[239],"best":[241],"previous":[242],"complexity.":[261],"We":[262,318],"test":[263],"our":[264,273,321],"algorithms":[265,343],"randomly":[267],"uniform":[268],"point":[269],"sets":[270],"compare":[272,320],"against":[277],"Minimum":[279],"Steiner":[282,295],"(MRST)":[283],"approximation":[285,327],"algorithm.":[286],"Our":[287],"results":[288],"show":[289,340],"RDPTs":[291,312],"competitive":[293],"trees":[296],"wire\u2010length":[299],"when":[300],"number":[302],"less":[306],"than":[307],"32.":[308],"makes":[311],"VLSI":[315],"routing":[316],"also":[319],"Rao\u2010Shor":[325],"obtaining":[329],"improvements":[330],"up":[332],"10%":[334],"wirelength.":[337],"These":[338],"comparisons":[339],"herein":[345],"produce":[346],"promising":[347],"results.":[348]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
