{"id":"https://openalex.org/W7214906655","doi":"https://doi.org/10.48550/arxiv.2609.37528","title":"A Spatial Benders Algorithm for Delay Constrained Routing","display_name":"A Spatial Benders Algorithm for Delay Constrained Routing","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214906655","doi":"https://doi.org/10.48550/arxiv.2609.37528"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37528","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37528","pdf_url":"https://arxiv.org/pdf/2609.37528","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37528","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061303343","display_name":"Antonio Frangioni","orcid":"https://orcid.org/0000-0002-5704-3170","observed_orcids":["https://orcid.org/0000-0002-5704-3170"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Frangioni, Antonio","raw_affiliation_strings":["Dipartimento di Informatica , Universit\u00e0 di Pisa , Largo B. Pontecorvo 3 , 56127 Pisa , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica , Universit\u00e0 di Pisa , Largo B. Pontecorvo 3 , 56127 Pisa , Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043357839","display_name":"Laura Galli","orcid":"https://orcid.org/0000-0002-5801-9439","observed_orcids":["https://orcid.org/0000-0002-5801-9439"]},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Galli, Laura","raw_affiliation_strings":["Dipartimento di Matematica , Alma Mater Studiorum Universit\u00e0 di Bologna , Piazza di Porta San Donato 5 , 40126 Bologna , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica , Alma Mater Studiorum Universit\u00e0 di Bologna , Piazza di Porta San Donato 5 , 40126 Bologna , Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073118154","display_name":"Luca Mencarelli","orcid":"https://orcid.org/0009-0003-6005-6196","observed_orcids":["https://orcid.org/0009-0003-6005-6196"]},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Mencarelli, Luca","raw_affiliation_strings":["Dipartimento di Informatica , Universit\u00e0 di Pisa , Largo B. Pontecorvo 3 , 56127 Pisa , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica , Universit\u00e0 di Pisa , Largo B. Pontecorvo 3 , 56127 Pisa , Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5094294761","display_name":"Enrico Sorbera","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sorbera, Enrico","raw_affiliation_strings":["Dipartimento di Matematica , Universit\u00e0 di Trento , Via Sommarive 14 , 38123 Povo , Trento , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica , Universit\u00e0 di Trento , Via Sommarive 14 , 38123 Povo , Trento , Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.5756999850273132,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.5756999850273132,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":0.22419999539852142,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.16249999403953552,"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/delay-constrained-routing","display_name":"delay-constrained routing","score":0.9959999918937683},{"id":"https://openalex.org/keywords/ip-networks","display_name":"IP networks","score":0.6159999966621399},{"id":"https://openalex.org/keywords/quality-of-service","display_name":"quality of service","score":0.7680000066757202},{"id":"https://openalex.org/keywords/bandwidth-compression","display_name":"bandwidth reduction","score":0.8970000147819519},{"id":"https://openalex.org/keywords/mixed-integer-second-order-cone-programming","display_name":"mixed-integer second-order cone programming","score":0.9070000052452087},{"id":"https://openalex.org/keywords/benders-decomposition","display_name":"Benders decomposition","score":0.8700000047683716},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.7689999938011169},{"id":"https://openalex.org/keywords/double-decomposition","display_name":"double decomposition","score":0.7089999914169312},{"id":"https://openalex.org/keywords/spatial-branch-and-bound","display_name":"spatial branch-and-bound","score":0.8820000290870667}],"concepts":[{"id":"https://openalex.org/C44210515","wikidata":"https://www.wikidata.org/wiki/Q16968978","display_name":"Bespoke","level":2,"score":0.8012999892234802},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6050000190734863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5974000096321106},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5924000144004822},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.5382000207901001},{"id":"https://openalex.org/C84434228","wikidata":"https://www.wikidata.org/wiki/Q4531332","display_name":"Elmore delay","level":4,"score":0.5072000026702881},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4745999872684479},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C27665512","wikidata":"https://www.wikidata.org/wiki/Q3042795","display_name":"Benders' decomposition","level":2,"score":0.42820000648498535},{"id":"https://openalex.org/C5119721","wikidata":"https://www.wikidata.org/wiki/Q220501","display_name":"Quality of service","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C44000306","wikidata":"https://www.wikidata.org/wiki/Q244330","display_name":"Hinge","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.26980000734329224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26649999618530273},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37528","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37528","pdf_url":"https://arxiv.org/pdf/2609.37528","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.37528","doi":"https://doi.org/10.48550/arxiv.2609.37528","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37528","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37528","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37528","pdf_url":"https://arxiv.org/pdf/2609.37528","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"score":0.7207000255584717,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214906655.pdf","grobid_xml":"https://content.openalex.org/works/W7214906655.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415028948","https://openalex.org/W7222705379","https://openalex.org/W4239056672","https://openalex.org/W2068762076","https://openalex.org/W2344296803","https://openalex.org/W7096564560","https://openalex.org/W1490570703","https://openalex.org/W2475636836","https://openalex.org/W185966676","https://openalex.org/W2038129566"],"abstract_inverted_index":{"We":[0,83,139],"study":[1],"the":[2,39,46,51,100,104,115],"Delay":[3],"Constrained":[4],"Routing":[5],"(DCR)":[6],"problem":[7],"arising":[8],"in":[9,36,50,119,151],"IP":[10,23],"computer":[11],"networks":[12],"to":[13,21,27,30,80],"support":[14],"high":[15],"bandwidth":[16,49],"applications.":[17],"The":[18],"goal":[19],"is":[20],"route":[22],"packets,":[24],"from":[25],"source":[26],"destination,":[28],"subject":[29],"quality":[31],"of":[32,103,114],"service":[33],"constraints":[34],"--":[35,43],"particular,":[37,107],"bounding":[38],"worst":[40],"case":[41],"delay":[42],"while":[44,68],"minimizing":[45],"total":[47],"allocated":[48],"network.":[52],"DCR":[53],"can":[54],"be":[55],"formulated":[56],"as":[57],"a":[58,85,94,110,120,130],"Mixed-Integer":[59],"Second-Order":[60],"Cone":[61],"Program,":[62],"and":[63,76,148],"solved":[64],"using":[65,135],"standard":[66],"solvers;":[67],"generally":[69],"efficient,":[70],"this":[71],"hinges":[72],"on":[73],"off-the-shelf":[74],"tools":[75],"does":[77],"not":[78],"scale":[79],"large":[81],"instances.":[82],"devise":[84],"solver-free":[86],"bespoke":[87,131],"approach":[88,97,134,143],"that":[89,98,117,141],"uses":[90],"nested":[91],"Benders-Lagrange,":[92],"namely,":[93],"double":[95],"decomposition":[96],"exploits":[99],"special":[101],"structure":[102],"problem.":[105],"In":[106],"we":[108,127],"use":[109],"nonconvex":[111,121],"nonlinear":[112],"formulation":[113],"problem,":[116],"results":[118],"Benders":[122],"value":[123],"function":[124],"whose":[125],"optimization":[126],"tackle":[128],"with":[129],"Spatial":[132],"Branch-and-Bound":[133],"custom":[136],"piecewise-convex":[137],"cuts.":[138],"show":[140],"our":[142],"provides":[144],"very":[145],"tight":[146],"upper":[147],"lower":[149],"bounds":[150],"competitive":[152],"running":[153],"times":[154],"w.r.t.":[155],"previous":[156],"state-of-the-art":[157],"approaches.":[158]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-01T00:00:00"}