{"id":"https://openalex.org/W4287816460","doi":"https://doi.org/10.4230/lipics.socg.2026.46","title":"A Branch-And-Bound Algorithm for the Traveling Salesman Problem with Difficult Neighborhoods","display_name":"A Branch-And-Bound Algorithm for the Traveling Salesman Problem with Difficult Neighborhoods","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W4287816460","doi":"https://doi.org/10.4230/lipics.socg.2026.46"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25852","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.46/LIPIcs.SoCG.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.46/LIPIcs.SoCG.2026.46.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015542807","display_name":"S\u00e1ndor P. Fekete","orcid":"https://orcid.org/0000-0002-9062-4241"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fekete, S\u00e1ndor P.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Kniep, Rouven","orcid":null},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kniep, Rouven","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073066645","display_name":"Dominik Krupke","orcid":"https://orcid.org/0000-0003-1573-3496"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Krupke, Dominik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Perk, Michael","orcid":null},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Perk, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0010923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9840999841690063,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9700000286102295,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.9101166725158691},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6945351958274841},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6449910998344421},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5967305898666382},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.5855467319488525},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5664651989936829},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5572331547737122},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5054795742034912},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.49321216344833374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48115622997283936},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.45756322145462036},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4541638493537903},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4324200749397278},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3446459174156189},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.20209789276123047},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.11285704374313354}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.9101166725158691},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6945351958274841},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6449910998344421},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5967305898666382},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.5855467319488525},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5664651989936829},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5572331547737122},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5054795742034912},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.49321216344833374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48115622997283936},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.45756322145462036},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4541638493537903},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4324200749397278},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3446459174156189},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.20209789276123047},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.11285704374313354},{"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/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25852","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.46/LIPIcs.SoCG.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"pmh:doi:10.4230/lipics.socg.2026.46","is_oa":true,"landing_page_url":"https://books.google.de/books?id=mYm0bLd3fcoC","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25852","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.46/LIPIcs.SoCG.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5199999809265137,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4287816460.pdf","grobid_xml":"https://content.openalex.org/works/W4287816460.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2300145982","https://openalex.org/W2363904277","https://openalex.org/W2580512045","https://openalex.org/W2375652826","https://openalex.org/W2365830408","https://openalex.org/W1569666406","https://openalex.org/W868123585","https://openalex.org/W4296997005","https://openalex.org/W1500255470","https://openalex.org/W2048874717"],"abstract_inverted_index":{"The":[0],"Traveling":[1,10],"Salesman":[2,11],"Problem":[3,12],"with":[4,103,165,180,215,220],"Neighborhoods":[5],"(TSPN)":[6],"generalizes":[7],"the":[8,38,55,98,181,213,221],"classical":[9],"(TSP)":[13],"by":[14],"requiring":[15],"a":[16,20,29,86,91,113,174],"tour":[17],"to":[18,65,75,81,121,129,167,205],"visit":[19],"set":[21],"of":[22,52,93,100,116,134,156,192,203,212],"polygonal":[23,124],"regions":[24,77],"rather":[25],"than":[26,127],"fixed":[27],"points,":[28],"natural":[30],"goal":[31],"that":[32,89],"arises":[33],"in":[34,62,141],"various":[35],"applications.":[36],"While":[37],"geometric":[39],"TSP":[40],"allows":[41,119,200],"arbitrarily":[42],"close":[43],"approximation":[44],"and":[45,67,143],"provably":[46],"optimal":[47,110],"solutions":[48],"for":[49,69,112],"benchmark":[50,72,163],"instances":[51,73,126,164,184,191,204,214],"significant":[53],"size,":[54],"TSPN":[56,125],"is":[57],"considerably":[58],"more":[59],"challenging,":[60],"both":[61],"theory":[63,142],"(due":[64],"APX-hardness)":[66],"practice,":[68],"which":[70],"only":[71,210],"up":[74,166],"16":[76],"have":[78],"been":[79],"solved":[80,185],"optimality.":[82],"Here":[83],"we":[84,150],"present":[85],"branch-and-bound":[87],"algorithm":[88],"combines":[90],"spectrum":[92],"geometry-based":[94],"filters":[95],"(for":[96,108],"reducing":[97],"number":[99],"considered":[101],"sequences)":[102],"Second-Order":[104],"Cone":[105],"Programs":[106],"(SOCP)":[107],"computing":[109],"tours":[111],"given":[114],"permutation":[115],"neighborhoods).":[117],"This":[118],"us":[120],"solve":[122],"larger":[123,190],"before":[128],"within":[130,178,186,207],"an":[131],"optimality":[132,176,206,216],"tolerance":[133],"0.1%;":[135],"moreover,":[136],"while":[137],"previous":[138],"work":[139],"(both":[140],"practice)":[144],"relied":[145],"on":[146,161],"relatively":[147],"benign":[148],"neighborhoods,":[149],"can":[151],"handle":[152],"non-convex,":[153],"non-simple":[154],"neighborhoods":[155],"different":[157],"sizes.":[158],"In":[159],"experiments":[160],"490":[162],"50":[168],"polygons":[169],"each,":[170],"our":[171,197],"method":[172,198],"achieves":[173],"99.6%":[175],"rate":[177],"300s,":[179],"remaining":[182],"two":[183],"595s.":[187],"For":[188],"68":[189],"size":[193],"n":[194],"=":[195],"60,":[196],"still":[199],"solving":[201],"86.8%":[202],"900s,":[208],"leaving":[209],"3":[211],"gaps":[217],"above":[218],"3%,":[219],"maximum":[222],"being":[223],"5.53%.":[224]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2022-07-26T00:00:00"}