{"id":"https://openalex.org/W7131374110","doi":"https://doi.org/10.48550/arxiv.2602.21088","title":"A Space-space Trade-off for Directed st-Connectivity","display_name":"A Space-space Trade-off for Directed st-Connectivity","publication_year":2026,"publication_date":"2026-02-24","ids":{"openalex":"https://openalex.org/W7131374110","doi":"https://doi.org/10.48550/arxiv.2602.21088"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.21088","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Edenhofer, Roman","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edenhofer, Roman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"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":0.5723000168800354,"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":0.5723000168800354,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.16979999840259552,"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/T12288","display_name":"Optimization and Search Problems","score":0.031599998474121094,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.526199996471405},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5260000228881836},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.517300009727478},{"id":"https://openalex.org/keywords/workspace","display_name":"Workspace","score":0.49320000410079956},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.43230000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5968999862670898},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.526199996471405},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5260000228881836},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C58581272","wikidata":"https://www.wikidata.org/wiki/Q12741163","display_name":"Workspace","level":3,"score":0.49320000410079956},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4596000015735626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.446399986743927},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36570000648498535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32350000739097595},{"id":"https://openalex.org/C161790260","wikidata":"https://www.wikidata.org/wiki/Q82264","display_name":"Catalysis","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2822999954223633}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.21088","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.21088","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.21088","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.21088","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,57,71,75,123],"space-space":[3],"trade-off":[4],"for":[5,97],"directed":[6,25],"$st$-connectivity":[7,26],"in":[8],"the":[9,48,82,91,114],"catalytic":[10,43,58,68,76,98],"space":[11],"model.":[12],"For":[13],"any":[14],"integer":[15],"$k":[16],"\\leq":[17],"n$,":[18],"we":[19,73],"give":[20],"an":[21],"algorithm":[22,55,80],"that":[23],"decides":[24],"using":[27],"$O(\\log":[28,61],"n":[29],"\\cdot":[30,38],"\\log":[31],"k+\\log":[32],"n)$":[33,62,67],"regular":[34],"workspace":[35,63],"and":[36,56,64,104],"$O\\left(\\frac{n}{k}":[37],"\\log^2":[39,66],"n\\right)$":[40],"bits":[41],"of":[42,78,116,122],"memory.":[44,69],"This":[45],"interpolates":[46],"between":[47],"classical":[49],"$O(\\log^2":[50],"n)$-space":[51],"bound":[52],"from":[53,118],"Savitch's":[54,79],"endpoint":[59,83],"with":[60],"$O(n\\cdot":[65],"As":[70],"warm-up,":[72],"present":[74],"variant":[77],"achieving":[81],"above.":[84],"Up":[85],"to":[86,102,112,120],"logarithmic":[87],"factors,":[88],"this":[89],"matches":[90],"smallest":[92],"catalyst":[93],"size":[94],"currently":[95],"known":[96],"logspace":[99],"algorithms,":[100],"due":[101],"Cook":[103],"Pyne":[105],"(ITCS":[106],"2026).":[107],"Our":[108],"techniques":[109],"also":[110],"extend":[111],"counting":[113],"number":[115],"walks":[117],"$s$":[119],"$t$":[121],"given":[124],"length":[125],"$\\ell\\leq":[126],"n$.":[127]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-02-26T00:00:00"}