{"id":"https://openalex.org/W7211879528","doi":"https://doi.org/10.48550/arxiv.2609.04825","title":"Beyond Distance Ordering: Resource Complexity and Universal Optimality of Exact Labeled Directed Shortest Paths","display_name":"Beyond Distance Ordering: Resource Complexity and Universal Optimality of Exact Labeled Directed Shortest Paths","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211879528","doi":"https://doi.org/10.48550/arxiv.2609.04825"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04825","pdf_url":"https://arxiv.org/pdf/2609.04825","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/2609.04825","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150575830","display_name":"Bin Cai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Cai, Bin","raw_affiliation_strings":["Wuhan University of Technology Wuhan , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan University of Technology Wuhan , China","institution_ids":["https://openalex.org/I196699116"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5150575830"],"corresponding_institution_ids":["https://openalex.org/I196699116"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T10374","display_name":"Advanced Graph Theory Research","score":9.999999747378752e-05,"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/single-source-shortest-path","display_name":"single-source shortest path","score":0.8370000123977661},{"id":"https://openalex.org/keywords/resource-complexity","display_name":"resource complexity","score":0.6909999847412109},{"id":"https://openalex.org/keywords/universal-optimality","display_name":"universal optimality","score":0.7739999890327454},{"id":"https://openalex.org/keywords/directed-graphs","display_name":"directed graphs","score":0.48500001430511475},{"id":"https://openalex.org/keywords/dags","display_name":"DAGs","score":0.6370000243186951},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.7049999833106995},{"id":"https://openalex.org/keywords/deterministic-algorithms","display_name":"deterministic algorithms","score":0.3089999854564667},{"id":"https://openalex.org/keywords/competitive-analysis","display_name":"competitive analysis","score":0.34299999475479126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6531999707221985},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.430400013923645},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.4140999913215637},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.412200003862381},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.37709999084472656},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33660000562667847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31049999594688416},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.25769999623298645}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04825","pdf_url":"https://arxiv.org/pdf/2609.04825","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.2609.04825","doi":"https://doi.org/10.48550/arxiv.2609.04825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04825","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:2609.04825","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04825","pdf_url":"https://arxiv.org/pdf/2609.04825","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211879528.pdf","grobid_xml":"https://content.openalex.org/works/W7211879528.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2014612701"],"related_works":["https://openalex.org/W188705541","https://openalex.org/W1991063612","https://openalex.org/W2055906662","https://openalex.org/W2185114784","https://openalex.org/W1982630055","https://openalex.org/W1638040061","https://openalex.org/W1988593903","https://openalex.org/W1974409198","https://openalex.org/W2020556531","https://openalex.org/W2061135810"],"abstract_inverted_index":{"We":[0],"study":[1],"exact":[2,82,150],"single-source":[3],"shortest":[4],"paths":[5],"when":[6,128],"the":[7,11,23,28,41,54,70,76,101,112,131,145,184],"output":[8],"is":[9,39,80],"only":[10],"materialized":[12],"labeled":[13],"distance":[14,20],"vector":[15],"($\\mathrm{DIST}$),":[16],"rather":[17],"than":[18],"a":[19,88],"order.":[21],"In":[22],"full":[24,77],"deterministic":[25,119,186],"comparison-addition":[26],"model,":[27],"minimum":[29],"worst-case":[30],"number":[31,43],"of":[32,45],"additions":[33],"on":[34,73,163],"every":[35,164],"fixed":[36],"directed":[37],"topology":[38],"exactly":[40],"maximum":[42],"$\u03c1_{\\mathrm{fwd}}$":[44],"forward":[46],"nonsource":[47],"endpoint":[48],"classes":[49],"over":[50],"rooted":[51],"vertex":[52],"orders;":[53],"lower":[55],"bound":[56,188],"permits":[57],"adaptive":[58],"control,":[59],"literals,":[60],"and":[61,115,183],"arbitrary":[62],"mixed":[63],"sums.":[64],"This":[65],"arithmetic":[66],"law":[67],"aligns":[68],"with":[69,124],"comparison":[71],"optimum":[72,114],"DAGs,":[74],"where":[75,122],"resource":[78],"region":[79],"an":[81,117,180,190],"rectangle.":[83],"Cycles":[84],"destroy":[85],"that":[86],"alignment:":[87],"two-spoke":[89],"shared-hub":[90],"graph":[91],"has":[92,116],"coordinatewise":[93,133],"optima":[94],"$(4,2)$":[95],"but":[96,174],"requires":[97],"five":[98],"comparisons":[99,110],"at":[100,111],"two-addition":[102],"budget.":[103],"Its":[104],"$k$-spoke":[105],"extension":[106],"forces":[107],"$k\\log_2":[108],"k+O(k)$":[109],"addition":[113],"entropy-tight":[118],"tradeoff":[120],"$C_{k+r}^*(H_k)=\u0398(k+\u039b_{k,r})$,":[121],"$\u039b_{k,r}=\\log_2(k!/[r!(r+1)^{k-r}])$,":[123],"leading":[125],"constant":[126],"one":[127,139,154],"$\u039b_{k,r}/k\\to\\infty$.":[129],"Because":[130],"two":[132],"minima":[134],"need":[135],"not":[136],"belong":[137],"to":[138,144],"program,":[140],"these":[141],"conflicts":[142],"lead":[143],"same-program":[146],"benchmark":[147],"$\\operatorname{OPT}_{\\mathrm{DIST}}=\\inf_A\\sup_w(C_A(w)+P_A(w))$.":[148],"An":[149],"transcript-cone":[151],"game":[152],"yields":[153],"uniform":[155,192],"interpreter":[156],"whose":[157],"charged":[158],"addition-comparison":[159],"cost":[160],"equals":[161],"$\\operatorname{OPT}_{\\mathrm{DIST}}$":[162],"topology;":[165],"its":[166],"optimal":[167,197],"actions":[168],"are":[169],"synthesizable":[170],"in":[171],"polynomial":[172],"space":[173],"may":[175],"require":[176],"exponential":[177],"time.":[178],"Finally,":[179],"active-core":[181],"reduction":[182],"current":[185],"directed-SSSP":[187],"give":[189],"efficient":[191,203],"$O\\!\\bigl(\\operatorname{OPT}_{\\mathrm{DIST}}\\sqrt{\\log(2+\\operatorname{OPT}_{\\mathrm{DIST}})\\log\\log(4+\\operatorname{OPT}_{\\mathrm{DIST}})}\\bigr)$":[193],"charged-operation":[194],"bound.":[195],"Thus":[196],"numerical":[198],"policies":[199],"exist":[200],"uniformly,":[201],"while":[202],"constant-competitive":[204],"navigation":[205],"remains":[206],"open.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}