{"id":"https://openalex.org/W3091197103","doi":"https://doi.org/10.1109/icra40945.2020.9196917","title":"Sample Complexity of Probabilistic Roadmaps via \u03b5-nets","display_name":"Sample Complexity of Probabilistic Roadmaps via \u03b5-nets","publication_year":2020,"publication_date":"2020-05-01","ids":{"openalex":"https://openalex.org/W3091197103","doi":"https://doi.org/10.1109/icra40945.2020.9196917","mag":"3091197103"},"language":"en","primary_location":{"id":"doi:10.1109/icra40945.2020.9196917","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra40945.2020.9196917","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Robotics and Automation (ICRA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108766687","display_name":"Matthew Tsao","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Matthew Tsao","raw_affiliation_strings":["Autonomous Systems Laboratory, Stanford University, CA, USA"],"affiliations":[{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000480439","display_name":"Kiril Solovey","orcid":"https://orcid.org/0000-0003-0254-0572"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kiril Solovey","raw_affiliation_strings":["Autonomous Systems Laboratory, Stanford University, CA, USA"],"affiliations":[{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050003000","display_name":"Marco Pavone","orcid":"https://orcid.org/0000-0002-0206-4337"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marco Pavone","raw_affiliation_strings":["Autonomous Systems Laboratory, Stanford University, CA, USA"],"affiliations":[{"raw_affiliation_string":"Autonomous Systems Laboratory, Stanford University, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108766687"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":0.8793,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.76591383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2196","last_page":"2202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9994000196456909,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9994000196456909,"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/T10142","display_name":"Formal Methods in Verification","score":0.9958000183105469,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/completeness","display_name":"Completeness (order theory)","score":0.7863532900810242},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6828742623329163},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5056774616241455},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.5011122226715088},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.4816214442253113},{"id":"https://openalex.org/keywords/motion-planning","display_name":"Motion planning","score":0.467816561460495},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45750856399536133},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.44870391488075256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4471629858016968},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4403451681137085},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.44025444984436035},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.42950087785720825},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.42099589109420776},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4189956784248352},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41004854440689087},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3902389109134674},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3539169430732727},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15178588032722473},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09965106844902039},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09727886319160461}],"concepts":[{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7863532900810242},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6828742623329163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5056774616241455},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.5011122226715088},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.4816214442253113},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.467816561460495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45750856399536133},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.44870391488075256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4471629858016968},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4403451681137085},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.44025444984436035},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.42950087785720825},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.42099589109420776},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4189956784248352},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41004854440689087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3902389109134674},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3539169430732727},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15178588032722473},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09965106844902039},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09727886319160461},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icra40945.2020.9196917","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra40945.2020.9196917","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 IEEE International Conference on Robotics and Automation (ICRA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1014665884","https://openalex.org/W1424654272","https://openalex.org/W1501654049","https://openalex.org/W1578640434","https://openalex.org/W1587371456","https://openalex.org/W1712772804","https://openalex.org/W1814533834","https://openalex.org/W1864112212","https://openalex.org/W1971086298","https://openalex.org/W1986004895","https://openalex.org/W1991435017","https://openalex.org/W2096636360","https://openalex.org/W2101993361","https://openalex.org/W2114306020","https://openalex.org/W2128990851","https://openalex.org/W2399501438","https://openalex.org/W2490090381","https://openalex.org/W2628084930","https://openalex.org/W2808763600","https://openalex.org/W2885010347","https://openalex.org/W2886374915","https://openalex.org/W2949117375","https://openalex.org/W2953928214","https://openalex.org/W2955697550","https://openalex.org/W2962805470","https://openalex.org/W2963047720","https://openalex.org/W2963409832","https://openalex.org/W2963439114","https://openalex.org/W2963659407","https://openalex.org/W3021764030","https://openalex.org/W3103346840","https://openalex.org/W3104605181","https://openalex.org/W3104996132","https://openalex.org/W3106159194","https://openalex.org/W3106241941","https://openalex.org/W4236470048","https://openalex.org/W6637540238","https://openalex.org/W6713241665","https://openalex.org/W6739879031","https://openalex.org/W6744470484","https://openalex.org/W6786780223"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W4229993731","https://openalex.org/W2381059884","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2998581040","https://openalex.org/W2220405813","https://openalex.org/W2610708416","https://openalex.org/W2374111230"],"abstract_inverted_index":{"We":[0,42],"study":[1],"fundamental":[2],"theoretical":[3],"aspects":[4],"of":[5,24,46,49,61,87,93,100,124],"probabilistic":[6],"roadmaps":[7],"(PRM)":[8],"in":[9,91,109,120],"the":[10,25,30,44,50,80,85,98,117,122,142],"finite":[11],"time":[12],"(non-asymptotic)":[13],"regime.":[14],"In":[15,129],"particular,":[16],"we":[17,89,131],"investigate":[18],"how":[19],"completeness":[20],"and":[21,36,95],"optimality":[22],"guarantees":[23],"approach":[26],"are":[27],"influenced":[28],"by":[29,137],"underlying":[31],"deterministic":[32],"sampling":[33,134],"distribution":[34,135],"X":[35],"connection":[37],"radius":[38],"r":[39,71],">":[40,66],"0.":[41],"develop":[43],"notion":[45],"(\u03b4,":[47,105],"\u03b5)-completeness":[48],"parameters":[51],"X,":[52,70],"r,":[53],"which":[54,114,121],"indicates":[55],"that":[56,139],"for":[57],"every":[58],"motion-planning":[59],"problem":[60],"clearance":[62],"at":[63],"least":[64],"\u03b4":[65],"0,":[67],"PRM":[68],"using":[69,148],"returns":[72],"a":[73,133],"solution":[74],"no":[75],"longer":[76],"than":[77],"1+\u03b5":[78],"times":[79],"shortest":[81],"\u03b4-clear":[82],"path.":[83],"Leveraging":[84],"concept":[86],"e-nets,":[88],"characterize":[90],"terms":[92],"lower":[94],"upper":[96],"bounds":[97],"number":[99,123],"samples":[101,125],"needed":[102],"to":[103,127],"guarantee":[104],"\u03b5)-completeness.":[106],"This":[107],"is":[108],"contrast":[110],"with":[111],"previous":[112],"work":[113],"mostly":[115],"considered":[116],"asymptotic":[118],"regime":[119],"tends":[126],"infinity.":[128],"practice,":[130],"propose":[132],"inspired":[136],"e-nets":[138],"achieves":[140],"nearly":[141],"same":[143],"coverage":[144],"as":[145],"grids":[146],"while":[147],"fewer":[149],"samples.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}