{"id":"https://openalex.org/W2082754619","doi":"https://doi.org/10.3390/a2031069","title":"How Many Lions Are Needed to Clear a Grid?","display_name":"How Many Lions Are Needed to Clear a Grid?","publication_year":2009,"publication_date":"2009-09-07","ids":{"openalex":"https://openalex.org/W2082754619","doi":"https://doi.org/10.3390/a2031069","mag":"2082754619"},"language":"en","primary_location":{"id":"doi:10.3390/a2031069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031069","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1069/pdf?version=1252399148","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/2/3/1069/pdf?version=1252399148","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036690026","display_name":"Florian Berger","orcid":"https://orcid.org/0000-0003-3355-4336"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Florian Berger","raw_affiliation_strings":["Institute of Computer Science, University of Bonn, 53117 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bonn, 53117 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050718381","display_name":"Alexander Gilbers","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Gilbers","raw_affiliation_strings":["Institute of Computer Science, University of Bonn, 53117 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bonn, 53117 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071308897","display_name":"Ansgar Gr\u00fcne","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ansgar Gr\u00fcne","raw_affiliation_strings":["Institute of Computer Science, University of Bonn, 53117 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bonn, 53117 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109226564","display_name":"Rolf Klein","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rolf Klein","raw_affiliation_strings":["Institute of Computer Science, University of Bonn, 53117 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, University of Bonn, 53117 Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5036690026"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.5488,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89324074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2","issue":"3","first_page":"1069","last_page":"1086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9948999881744385,"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"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9523000121116638,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5850507020950317},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5415648818016052},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16528022289276123},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09230008721351624}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5850507020950317},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5415648818016052},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16528022289276123},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09230008721351624}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a2031069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031069","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1069/pdf?version=1252399148","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f1e2ae90b163463f92d9eb3f169cb220","is_oa":true,"landing_page_url":"https://doaj.org/article/f1e2ae90b163463f92d9eb3f169cb220","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 2, Iss 3, Pp 1069-1086 (2009)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/2/3/1069/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a2031069","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Algorithms; Volume 2; Issue 3; Pages: 1069-1086","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a2031069","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a2031069","pdf_url":"https://www.mdpi.com/1999-4893/2/3/1069/pdf?version=1252399148","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2082754619.pdf","grobid_xml":"https://content.openalex.org/works/W2082754619.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W584597337","https://openalex.org/W1998007106","https://openalex.org/W1999293408","https://openalex.org/W2021208601","https://openalex.org/W2028400828","https://openalex.org/W2028560778","https://openalex.org/W2038643780","https://openalex.org/W2058877225","https://openalex.org/W2137766675","https://openalex.org/W2139676984","https://openalex.org/W2395279694"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"We":[0],"consider":[1,71],"a":[2,13,35,45,96],"pursuit-evasion":[3],"problem":[4,74,97],"where":[5,99],"some":[6],"lions":[7,57,84,101],"have":[8],"the":[9,63,72,91,100],"task":[10],"to":[11,48,61,89,105,110],"clear":[12,62,90],"grid":[14,108,112],"graph":[15],"whose":[16],"nodes":[17],"are":[18,58,85,102],"initially":[19],"contaminated.":[20],"The":[21],"contamination":[22,43],"spreads":[23],"one":[24],"step":[25],"per":[26],"time":[27],"unit":[28],"in":[29,75],"each":[30],"direction":[31],"not":[32,59],"blocked":[33],"by":[34],"lion.":[36],"A":[37],"vertex":[38],"is":[39],"cleared":[40],"from":[41,107],"its":[42],"whenever":[44],"lion":[46],"moves":[47],"it.":[49],"Brass":[50],"et":[51],"al.":[52],"[5]":[53],"showed":[54],"that":[55,82],"n/2":[56],"enough":[60],"n":[64],"x":[65],"n-grid.":[66],"In":[67],"this":[68],"paper,":[69],"we":[70,94],"same":[73],"dimension":[76],"d":[77],"&gt;":[78],"2":[79],"and":[80,87],"prove":[81],"\u0398(nd-1/\u221ad)":[83],"necessary":[86],"sufficient":[88],"nd-grid.":[92],"Furthermore,":[93],"analyze":[95],"variant":[98],"also":[103],"allowed":[104],"jump":[106],"vertices":[109],"non-adjacent":[111],"vertices.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
