{"id":"https://openalex.org/W3006084812","doi":"https://doi.org/10.1007/978-3-030-48966-3_13","title":"Polynomial Time Algorithms for Tracking Path Problems","display_name":"Polynomial Time Algorithms for Tracking Path Problems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3006084812","doi":"https://doi.org/10.1007/978-3-030-48966-3_13","mag":"3006084812"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-48966-3_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-48966-3_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-48966-3_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-48966-3_13.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046990190","display_name":"Pratibha Choudhary","orcid":"https://orcid.org/0000-0002-1648-288X"},"institutions":[{"id":"https://openalex.org/I154549908","display_name":"Indian Institute of Technology Jodhpur","ror":"https://ror.org/03yacj906","country_code":"IN","type":"education","lineage":["https://openalex.org/I154549908"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ","IN"],"is_corresponding":true,"raw_author_name":"Pratibha Choudhary","raw_affiliation_strings":["Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic","Indian Institute of Technology Jodhpur , Jodhpur, India"],"affiliations":[{"raw_affiliation_string":"Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Indian Institute of Technology Jodhpur , Jodhpur, India","institution_ids":["https://openalex.org/I154549908"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046990190"],"corresponding_institution_ids":["https://openalex.org/I154549908","https://openalex.org/I44504214"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.3224,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60236435,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"84","issue":"6","first_page":"1548","last_page":"1570"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9987000226974487,"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":0.9980999827384949,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9926000237464905,"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/combinatorics","display_name":"Combinatorics","score":0.6925607323646545},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.5870509743690491},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5815465450286865},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5636317729949951},{"id":"https://openalex.org/keywords/tournament","display_name":"Tournament","score":0.5574209094047546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5466473698616028},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5184428691864014},{"id":"https://openalex.org/keywords/induced-path","display_name":"Induced path","score":0.501112699508667},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49440550804138184},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44768714904785156},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.44543319940567017},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.44543272256851196},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41253477334976196},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4066219627857208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3160440921783447}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6925607323646545},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.5870509743690491},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5815465450286865},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5636317729949951},{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.5574209094047546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5466473698616028},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5184428691864014},{"id":"https://openalex.org/C58228413","wikidata":"https://www.wikidata.org/wiki/Q15704639","display_name":"Induced path","level":5,"score":0.501112699508667},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49440550804138184},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44768714904785156},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.44543319940567017},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.44543272256851196},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41253477334976196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4066219627857208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3160440921783447},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"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/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/978-3-030-48966-3_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-48966-3_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-48966-3_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.1007/s00453-022-00931-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00931-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00931-1.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.07799","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.07799","pdf_url":"https://arxiv.org/pdf/2002.07799","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:3006084812","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.07799v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7254916","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7254916","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorial Algorithms","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2002.07799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.07799","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-48966-3_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-48966-3_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-48966-3_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3006084812.pdf","grobid_xml":"https://content.openalex.org/works/W3006084812.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1542244620","https://openalex.org/W1593793857","https://openalex.org/W1604521381","https://openalex.org/W1987849182","https://openalex.org/W1989633083","https://openalex.org/W2024517697","https://openalex.org/W2030087828","https://openalex.org/W2050579693","https://openalex.org/W2082806890","https://openalex.org/W2098361906","https://openalex.org/W2115589427","https://openalex.org/W2125838338","https://openalex.org/W2143479365","https://openalex.org/W2155061423","https://openalex.org/W2313696863","https://openalex.org/W2328184904","https://openalex.org/W2569646339","https://openalex.org/W2606478473","https://openalex.org/W2783129995","https://openalex.org/W2955033360","https://openalex.org/W2990235631","https://openalex.org/W3000559115","https://openalex.org/W3002948953","https://openalex.org/W3022173737","https://openalex.org/W3032082593","https://openalex.org/W3086608093","https://openalex.org/W3127361743","https://openalex.org/W4253053485","https://openalex.org/W6803021332"],"related_works":["https://openalex.org/W2955033360","https://openalex.org/W3086608093","https://openalex.org/W2783129995","https://openalex.org/W2957826768","https://openalex.org/W2126346711","https://openalex.org/W3006658084","https://openalex.org/W1481806052","https://openalex.org/W3098776817","https://openalex.org/W2518200572","https://openalex.org/W2918100086","https://openalex.org/W2802261039","https://openalex.org/W2038641767","https://openalex.org/W2149483831","https://openalex.org/W2953273474","https://openalex.org/W2061208844","https://openalex.org/W3123076862","https://openalex.org/W156319294","https://openalex.org/W2002764510","https://openalex.org/W2140226761","https://openalex.org/W3137352489"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,20,69,122,135,146,155,215],"graph":[3,143],"G":[4,144,176],",":[5,12,119,145,153,163,184],"and":[6,10,59,96,120,154,212],"terminal":[7],"vertices":[8,26],"s":[9],"t":[11],"the":[13,34,165,191,220],"Tracking":[14,51,80,86,103],"Paths":[15,52,81,87,104],"problem":[16],"asks":[17],"to":[18,27,179],"compute":[19],"set":[21,148],"of":[22,25,36,71,79,157,193,210],"minimum":[23],"number":[24],"be":[28],"marked":[29],"as":[30],"trackers,":[31],"such":[32],"that":[33,85,102,177],"sequence":[35,156],"trackers":[37,158],"encountered":[38],"in":[39,56,62,108,175],"each":[40],"$$s$$":[41,167,195],"<mml:math":[42,46,117,125,151,161,168,172,182,196,200],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>s</mml:mi></mml:math>":[43,169,197],"-":[44,170,198],"$$t$$":[45,171,199],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>t</mml:mi></mml:math>":[47,173,201],"path":[48,174],"is":[49,53,88,105],"unique.":[50],"NP":[54,106],"-hard":[55,107],"both":[57],"directed":[58],"undirected":[60,93,142],"graphs":[61,95,109],"general.":[63],"In":[64],"this":[65,130],"paper":[66],"we":[67,133,189,213],"give":[68,121,134,214],"collection":[70],"polynomial":[72,89,136,216],"time":[73,90,137,217],"algorithms":[74],"for":[75,92,129,219],"some":[76],"restricted":[77],"versions":[78],".":[82],"We":[83,99],"prove":[84],"solvable":[91],"chordal":[94],"tournament":[97],"graphs.":[98],"also":[100],"show":[101],"with":[110],"bounded":[111],"maximum":[112],"degree":[113],"$$\\Delta":[114],"\\ge":[115],"6$$":[116],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u0394</mml:mi><mml:mo>\u2265</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:math>":[118],"$$2(\\Delta":[123],"+1)$$":[124],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mn>2</mml:mn><mml:mo>(</mml:mo><mml:mi>\u0394</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>":[126],"-approximate":[127],"algorithm":[128,138,218],"case.":[131],"Further,":[132],"which,":[139],"given":[140],"an":[141],"tracking":[147,194],"$$T\\subseteq":[149],"V(G)$$":[150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>T</mml:mi><mml:mo>\u2286</mml:mo><mml:mi>V</mml:mi><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[152],"$$\\pi":[159,180],"$$":[160,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c0</mml:mi></mml:math>":[162,183],"returns":[164],"unique":[166],"corresponds":[178],"if":[185],"one":[186],"exists.":[187],"Finally":[188],"analyze":[190],"version":[192],"paths":[202,204],"where":[203],"are":[205],"tracked":[206],"using":[207],"edges":[208],"instead":[209],"vertices,":[211],"same.":[221]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}
