{"id":"https://openalex.org/W4417054814","doi":"https://doi.org/10.3390/a18120766","title":"Floyd\u2013Warshall Algorithm for Sparse Graphs","display_name":"Floyd\u2013Warshall Algorithm for Sparse Graphs","publication_year":2025,"publication_date":"2025-12-04","ids":{"openalex":"https://openalex.org/W4417054814","doi":"https://doi.org/10.3390/a18120766"},"language":"en","primary_location":{"id":"doi:10.3390/a18120766","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18120766","pdf_url":"https://www.mdpi.com/1999-4893/18/12/766/pdf?version=1764845630","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/18/12/766/pdf?version=1764845630","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093000776","display_name":"Dani Zugan","orcid":"https://orcid.org/0009-0006-8819-2538"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Dani Zugan","raw_affiliation_strings":["Faculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020534219","display_name":"Rok Po\u017ear","orcid":"https://orcid.org/0000-0002-2037-9535"},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Rok Po\u017ear","raw_affiliation_strings":["Andrej Maru\u0161i\u010d Institute, University of Primorska, 6000 Koper, Slovenia","Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, 6000 Koper, Slovenia","Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia"],"affiliations":[{"raw_affiliation_string":"Andrej Maru\u0161i\u010d Institute, University of Primorska, 6000 Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]},{"raw_affiliation_string":"Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, 6000 Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]},{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, 1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050751131","display_name":"Andrej Brodnik","orcid":"https://orcid.org/0000-0001-9773-0664"},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]},{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Andrej Brodnik","raw_affiliation_strings":["Andrej Maru\u0161i\u010d Institute, University of Primorska, 6000 Koper, Slovenia","Faculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia","Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, 6000 Koper, Slovenia"],"affiliations":[{"raw_affiliation_string":"Andrej Maru\u0161i\u010d Institute, University of Primorska, 6000 Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]},{"raw_affiliation_string":"Faculty of Computer and Information Science, University of Ljubljana, 1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, 6000 Koper, Slovenia","institution_ids":["https://openalex.org/I118905719"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5093000776"],"corresponding_institution_ids":["https://openalex.org/I153976015"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3950429,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"12","first_page":"766","last_page":"766"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.6886000037193298,"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"}},"topics":[{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.6886000037193298,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.2013999968767166,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.023099999874830246,"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/exploit","display_name":"Exploit","score":0.65829998254776},{"id":"https://openalex.org/keywords/dense-graph","display_name":"Dense graph","score":0.5796999931335449},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4772000014781952},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.4569000005722046},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4246000051498413},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.39149999618530273},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.38119998574256897},{"id":"https://openalex.org/keywords/graph-algorithms","display_name":"Graph algorithms","score":0.3720000088214874}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6606000065803528},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.65829998254776},{"id":"https://openalex.org/C13251829","wikidata":"https://www.wikidata.org/wiki/Q3085841","display_name":"Dense graph","level":5,"score":0.5796999931335449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5314000248908997},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4772000014781952},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44359999895095825},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4246000051498413},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C2986651925","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Graph algorithms","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.3652999997138977},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C5737132","wikidata":"https://www.wikidata.org/wiki/Q1101814","display_name":"Clique-width","level":5,"score":0.3109000027179718},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.2890999913215637},{"id":"https://openalex.org/C134727501","wikidata":"https://www.wikidata.org/wiki/Q5597073","display_name":"Graph bandwidth","level":5,"score":0.28859999775886536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27619999647140503},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C5134670","wikidata":"https://www.wikidata.org/wiki/Q1626444","display_name":"Cut","level":4,"score":0.26510000228881836}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a18120766","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18120766","pdf_url":"https://www.mdpi.com/1999-4893/18/12/766/pdf?version=1764845630","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:repozitorij.uni-lj.si:IzpisGradiva.php?id=177565","is_oa":true,"landing_page_url":"https://repozitorij.uni-lj.si/IzpisGradiva.php?id=177565","pdf_url":null,"source":{"id":"https://openalex.org/S4377196268","display_name":"Repository of the University of Ljubljana (University of Ljubljana)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I153976015","host_organization_name":"University of Ljubljana","host_organization_lineage":["https://openalex.org/I153976015"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 1999-4893","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:4750cc25a0a0470791a560d9abbc31fb","is_oa":true,"landing_page_url":"https://doaj.org/article/4750cc25a0a0470791a560d9abbc31fb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 12, p 766 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18120766","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18120766","pdf_url":"https://www.mdpi.com/1999-4893/18/12/766/pdf?version=1764845630","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417054814.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1982440947","https://openalex.org/W1991778515","https://openalex.org/W2006820476","https://openalex.org/W2007572995","https://openalex.org/W2008620264","https://openalex.org/W2058044254","https://openalex.org/W2084224084","https://openalex.org/W2090021115","https://openalex.org/W2104734478","https://openalex.org/W2116039228","https://openalex.org/W2118382442","https://openalex.org/W2133768189","https://openalex.org/W2169528473","https://openalex.org/W3155021337","https://openalex.org/W4387784321","https://openalex.org/W4413989710"],"related_works":[],"abstract_inverted_index":{"The":[0],"Floyd\u2013Warshall":[1],"algorithm,":[2],"which":[3],"uses":[4],"a":[5,11,42,47],"classic":[6],"dynamic":[7],"programming":[8],"approach,":[9],"provides":[10],"solution":[12],"to":[13,36,60],"the":[14,51,62,65,79],"all-pairs":[15],"shortest":[16],"paths":[17],"problem.":[18],"However,":[19],"for":[20],"sparse":[21],"graphs,":[22],"iteratively":[23],"applying":[24],"Dijkstra\u2019s,":[25],"or":[26],"some":[27],"other":[28],"similar":[29],"algorithm":[30],"from":[31,78],"each":[32],"node,":[33],"often":[34],"proves":[35],"be":[37],"more":[38],"efficient.":[39],"We":[40],"introduce":[41],"novel":[43],"technique":[44],"based":[45],"on":[46,72,99],"structural":[48],"decomposition":[49],"of":[50,64],"input":[52],"graph":[53,66],"into":[54],"strongly":[55],"connected":[56],"components,":[57],"allowing":[58],"us":[59],"exploit":[61],"disconnectedness":[63],"by":[67],"avoiding":[68],"redundant":[69],"relaxation":[70],"attempts":[71],"nodes":[73],"that":[74,93],"are":[75],"not":[76],"reachable":[77],"source":[80],"component.":[81],"Using":[82],"an":[83],"empirical":[84],"evaluation,":[85],"where":[86],"execution":[87],"time":[88],"is":[89],"measured,":[90],"we":[91],"demonstrate":[92],"our":[94],"approach":[95],"outperforms":[96],"existing":[97],"alternatives":[98],"disconnected":[100],"graphs.":[101]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-12-05T00:00:00"}
