{"id":"https://openalex.org/W7225791098","doi":"https://doi.org/10.5281/zenodo.24142495","title":"Offline Reachability in Directed Acyclic Graphs under Vertex Failures","display_name":"Offline Reachability in Directed Acyclic Graphs under Vertex Failures","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225791098","doi":"https://doi.org/10.5281/zenodo.24142495"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24142495","doi":"https://doi.org/10.5281/zenodo.24142495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24142495","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24142495","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5145917721","display_name":"Idris Ali Shaik","orcid":"https://orcid.org/0009-0009-9699-9712","observed_orcids":["https://orcid.org/0009-0009-9699-9712"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shaik, Idris Ali","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5145917721"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9657999873161316,"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":0.9657999873161316,"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":0.021299999207258224,"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":0.009399999864399433,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8647000193595886},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7458999752998352},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6610999703407288},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.6122000217437744},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5932999849319458},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5647000074386597},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.46470001339912415},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.41119998693466187},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.367900013923645},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.34769999980926514},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.33009999990463257},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31189998984336853},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27079999446868896},{"id":"https://openalex.org/C129691609","wikidata":"https://www.wikidata.org/wiki/Q3088151","display_name":"Transitive reduction","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.26420000195503235},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.25999999046325684}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24142495","doi":"https://doi.org/10.5281/zenodo.24142495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24142495","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24142496","doi":"https://doi.org/10.5281/zenodo.24142496","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24142496","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24142495","doi":"https://doi.org/10.5281/zenodo.24142495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24142495","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,176],"study":[1,178],"an":[2],"offline":[3],"reachability":[4,162],"problem":[5],"in":[6,146],"a":[7,12,26,35,38,139,190],"directed":[8],"acyclic":[9],"graph:":[10],"given":[11],"common":[13],"source":[14],"and":[15,59,65,68,82,91,107,157,210],"failure":[16],"sets":[17,116],"paired":[18],"with":[19,50],"target":[20,66,92],"sets,":[21],"does":[22],"any":[23],"query":[24],"retain":[25],"reachable":[27],"target?":[28],"This":[29],"is":[30],"linearly":[31],"equivalent":[32],"to":[33,37],"finding":[34],"path":[36],"labelled":[39],"terminal":[40],"that":[41],"avoids":[42],"every":[43,72],"vertex":[44,149],"forbidding":[45],"its":[46],"label.":[47],"For":[48,71,153],"queries":[49,64],"at":[51,164,196,213],"most":[52],"two":[53],"failures,":[54],"let":[55],"V,":[56],"E,":[57,105],"q_b>=1":[58],"M":[60,108],"count":[61],"vertices,":[62],"arcs,":[63],"incidences,":[67],"put":[69],"S=V+E+q_b+M.":[70],"integer":[73],"tau>=1,":[74],"our":[75],"threshold":[76],"algorithm":[77],"uses":[78],"\u00d5(S+E":[79],"tau+(V+E)q_b/tau)":[80],"time":[81,103,119,131,205,216],"\u00d5(S+V":[83],"tau)":[84],"working":[85],"words,":[86],"counting":[87],"discovery,":[88],"edge":[89],"scans":[90],"aggregation.":[93],"Here":[94],"\u00d5":[95],"suppresses":[96],"polylogarithmic":[97,136],"factors.":[98],"Setting":[99],"tau=ceil(sqrt(q_b))":[100],"gives":[101,189],"\u00d5(V^(3/2))":[102],"when":[104],"q_b":[106],"are":[109],"O(V).":[110],"Exact":[111],"sharing":[112],"of":[113,180,199],"identical":[114],"stored":[115],"preserves":[117],"the":[118,133,151,184,214],"bound,":[120,217],"but":[121],"can":[122],"still":[123],"require":[124],"superlinear":[125],"space.":[126],"Further":[127],"algorithms":[128],"give":[129,160],"near-linear":[130,211],"if":[132],"DAG":[134],"has":[135],"depth":[137],"or":[138],"supplied":[140],"partition":[141],"into":[142],"polylogarithmically":[143],"many":[144],"sequences":[145],"which":[147],"each":[148],"reaches":[150],"next.":[152],"unrestricted":[154],"multiplicity,":[155],"clique":[156],"directed-cycle":[158],"reductions":[159],"conditional":[161,191],"bounds":[163],"specified":[165],"label-count":[166],"regimes,":[167],"distinguishing":[168],"combinatorial":[169],"from":[170],"general":[171],"word":[172],"random-access":[173],"machine":[174],"algorithms.":[175],"also":[177],"falsification":[179],"guarded":[181],"Boolean":[182],"expressions:":[183],"listed":[185],"Hitting":[186],"Set":[187],"Conjecture":[188],"lower":[192],"bound":[193],"for":[194,206],"falsifying":[195],"least":[197],"one":[198],"several":[200],"shared":[201],"outputs.":[202],"Near-linear":[203],"total":[204],"arbitrary":[207],"two-failure":[208],"batches,":[209],"space":[212],"square-root-threshold":[215],"remain":[218],"open.":[219]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}