{"id":"https://openalex.org/W3183157744","doi":"https://doi.org/10.1145/3461477","title":"Approximate Counting of <i>k</i> -Paths: Simpler, Deterministic, and in Polynomial Space","display_name":"Approximate Counting of <i>k</i> -Paths: Simpler, Deterministic, and in Polynomial Space","publication_year":2021,"publication_date":"2021-07-15","ids":{"openalex":"https://openalex.org/W3183157744","doi":"https://doi.org/10.1145/3461477","mag":"3183157744"},"language":"en","primary_location":{"id":"doi:10.1145/3461477","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3461477","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3461477","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3461477","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038531405","display_name":"Daniel Lokshtanov","orcid":"https://orcid.org/0000-0002-3166-9212"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":["Lund University, Sweden"],"affiliations":[{"raw_affiliation_string":"Lund University, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038787166","display_name":"Andreas Bj\u00f6rklund","orcid":"https://orcid.org/0009-0009-9303-9986"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andreas Bj\u00d6rklund","raw_affiliation_strings":["University of California, Santa Barbara, United Stated"],"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, United Stated","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":["The Institute for Mathematical Sciences, HBNI and University of Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"The Institute for Mathematical Sciences, HBNI and University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082025487","display_name":"Meirav Zehavi","orcid":"https://orcid.org/0000-0002-3636-5322"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Meirav Zehavi","raw_affiliation_strings":["Ben-Gurion University, Israel"],"affiliations":[{"raw_affiliation_string":"Ben-Gurion University, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038531405"],"corresponding_institution_ids":["https://openalex.org/I187531555"],"apc_list":null,"apc_paid":null,"fwci":0.6058,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.72116656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"17","issue":"3","first_page":"1","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7695522308349609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7578484416007996},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.6827941536903381},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6660304665565491},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6019251346588135},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.5921846628189087},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5417916774749756},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47277358174324036},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47058406472206116},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4616185128688812},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.4475647509098053},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.440054714679718},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.42119699716567993},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41820842027664185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23445475101470947},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.15256139636039734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07793653011322021}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7695522308349609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7578484416007996},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.6827941536903381},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6660304665565491},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6019251346588135},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.5921846628189087},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5417916774749756},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47277358174324036},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47058406472206116},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4616185128688812},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.4475647509098053},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.440054714679718},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.42119699716567993},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41820842027664185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23445475101470947},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.15256139636039734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07793653011322021},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3461477","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3461477","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3461477","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:lup.lub.lu.se:33da8859-e245-43c4-a8c5-b8bb2fe61b13","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/33da8859-e245-43c4-a8c5-b8bb2fe61b13","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1549-6325","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/3461477","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3461477","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3461477","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1967155517","display_name":null,"funder_award_id":"176/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G267355722","display_name":null,"funder_award_id":"DST/SJF/MSA-01/2017-18","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4041286982","display_name":null,"funder_award_id":"76/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G5730270640","display_name":null,"funder_award_id":"2018302","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G6299013311","display_name":null,"funder_award_id":"2017-18","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G7702557058","display_name":null,"funder_award_id":"1176/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G8597347167","display_name":null,"funder_award_id":"2008838","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3183157744.pdf","grobid_xml":"https://content.openalex.org/works/W3183157744.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W118014313","https://openalex.org/W1190319202","https://openalex.org/W1531592115","https://openalex.org/W1575411448","https://openalex.org/W1643506661","https://openalex.org/W1808823193","https://openalex.org/W1842913573","https://openalex.org/W1852383912","https://openalex.org/W1966893452","https://openalex.org/W1980074516","https://openalex.org/W1996791172","https://openalex.org/W2003652380","https://openalex.org/W2048068744","https://openalex.org/W2065888137","https://openalex.org/W2067883080","https://openalex.org/W2092088134","https://openalex.org/W2100239335","https://openalex.org/W2102039892","https://openalex.org/W2104009289","https://openalex.org/W2104468092","https://openalex.org/W2120141762","https://openalex.org/W2129939288","https://openalex.org/W2137874581","https://openalex.org/W2152732502","https://openalex.org/W2153624566","https://openalex.org/W2196811896","https://openalex.org/W2216833188","https://openalex.org/W2296148711","https://openalex.org/W2408491755","https://openalex.org/W2596605817","https://openalex.org/W2605336159","https://openalex.org/W2610844084","https://openalex.org/W2621648198","https://openalex.org/W2779680819","https://openalex.org/W2909144890","https://openalex.org/W2953017342","https://openalex.org/W2963965405","https://openalex.org/W3139078859","https://openalex.org/W4210733105","https://openalex.org/W4245755206"],"related_works":["https://openalex.org/W2007715402","https://openalex.org/W2004524662","https://openalex.org/W2899261484","https://openalex.org/W1525123833","https://openalex.org/W2036758175","https://openalex.org/W1552026372","https://openalex.org/W2962985337","https://openalex.org/W3184929353","https://openalex.org/W1972433940","https://openalex.org/W3176273763"],"abstract_inverted_index":{"Recently,":[0],"Brand":[1],"et":[2],"al.":[3],"[STOC":[4],"2018]":[5],"gave":[6],"a":[7,29,34,77,111,116,125],"randomized":[8,126],"mathcal":[9],"O(4":[10],"k":[11,26,80,84,86,119,128,131,133],"m":[12,92,137,156],"\u03b5":[13,40,89],"-2":[14],"-time":[15,93,138],"exponential-space":[16],"algorithm":[17,60,107,142],"to":[18,33,46,172],"approximately":[19],"compute":[20],"the":[21,52,59,71,98,102,150,158,163],"number":[22,159,164],"of":[23,37,101,149,160,165,175,178],"paths":[24],"on":[25,42,118],"vertices":[27,161],"in":[28],"graph":[30,113],"G":[31,114],"up":[32],"multiplicative":[35],"error":[36],"1":[38],"\u00b1":[39],"based":[41],"exterior":[43],"algebra.":[44],"Prior":[45],"our":[47,169],"work,":[48],"this":[49,55],"has":[50,115],"been":[51],"state-of-the-art.":[53],"In":[54],"article,":[56],"we":[57,123],"revisit":[58],"by":[61],"Alon":[62],"and":[63,69,155,162],"Gutner":[64],"[IWPEC":[65],"2009,":[66],"TALG":[67],"2010],":[68],"obtain":[70],"following":[72],"results:":[73],"\u2022":[74,121],"We":[75],"present":[76,124],"deterministic":[78,105],"4":[79,127],"+":[81],"O":[82],"(\u221a":[83],"(log":[85,132],"+log":[87],"2":[88],"-1":[90,135],"))":[91,136],"polynomial-space":[94,106,139],"algorithm.":[95,140],"This":[96],"matches":[97],"running":[99],"time":[100],"best":[103],"known":[104],"for":[108],"deciding":[109],"whether":[110],"given":[112],"path":[117],"vertices.":[120],"Additionally,":[122,168],"+mathcal":[129],"O(log":[130],"+log\u03b5":[134],"Our":[141],"is":[143],"simple\u2014we":[144],"only":[145],"make":[146],"elementary":[147],"use":[148],"probabilistic":[151],"method.":[152],"Here,":[153],"n":[154],"are":[157],"edges,":[166],"respectively.":[167],"approach":[170],"extends":[171],"approximate":[173],"counting":[174],"other":[176],"patterns":[177],"small":[179],"size":[180],"(such":[181],"as":[182],"q":[183],"-dimensional":[184],"p":[185],"-matchings).":[186]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2021-08-02T00:00:00"}