{"id":"https://openalex.org/W2132884155","doi":"https://doi.org/10.1142/s1793830912500553","title":"ON <i>mRJ</i> REACHABILITY IN TREES","display_name":"ON <i>mRJ</i> REACHABILITY IN TREES","publication_year":2012,"publication_date":"2012-09-25","ids":{"openalex":"https://openalex.org/W2132884155","doi":"https://doi.org/10.1142/s1793830912500553","mag":"2132884155"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830912500553","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500553","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-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/A5088765097","display_name":"Biswajit Deb","orcid":"https://orcid.org/0000-0001-8689-9819"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"BISWAJIT DEB","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","institution_ids":["https://openalex.org/I1317621060"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#","institution_ids":["https://openalex.org/I1317621060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065965147","display_name":"Kalpesh Kapoor","orcid":"https://orcid.org/0000-0002-0242-3563"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"KALPESH KAPOOR","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","institution_ids":["https://openalex.org/I1317621060"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#","institution_ids":["https://openalex.org/I1317621060"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067185431","display_name":"Sukanta Pati","orcid":"https://orcid.org/0000-0002-8995-1894"},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"SUKANTA PATI","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India","institution_ids":["https://openalex.org/I1317621060"]},{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Guwahati, Assam 781039, India#TAB#","institution_ids":["https://openalex.org/I1317621060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088765097"],"corresponding_institution_ids":["https://openalex.org/I1317621060"],"apc_list":null,"apc_paid":null,"fwci":0.5491,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70258822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"04","issue":"04","first_page":"1250055","last_page":"1250055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T12288","display_name":"Optimization and Search Problems","score":0.9994000196456909,"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/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.8537824153900146},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6815711259841919},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5702095627784729},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5476644039154053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5174420475959778},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5154379606246948},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.48843422532081604},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44824251532554626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31646931171417236},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18045225739479065}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.8537824153900146},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6815711259841919},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5702095627784729},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5476644039154053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5174420475959778},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5154379606246948},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.48843422532081604},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44824251532554626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31646931171417236},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18045225739479065},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830912500553","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830912500553","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1930659875","https://openalex.org/W2015469394","https://openalex.org/W2034604437","https://openalex.org/W2100548703","https://openalex.org/W2122726981","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W2136512912","https://openalex.org/W2127267268","https://openalex.org/W2156446763","https://openalex.org/W2067910792","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W2889071233","https://openalex.org/W4321471459","https://openalex.org/W4221156924","https://openalex.org/W2154713079"],"abstract_inverted_index":{"Given":[0],"a":[1,4,19,25,55,59,67,75,90,98,132],"tree":[2,122,148],"T,":[3],"configuration":[5,133],"of":[6,37,78,96,146,186],"T":[7],"is":[8,18,48,74,123,137,157],"denoted":[9],"by":[10,61],"[Formula:":[11],"see":[12],"text]":[13],"which":[14,135],"represents":[15],"that":[16,45,168],"there":[17,130,165],"robot":[20,47,81,99,142],"at":[21,27],"the":[22,28,34,46,51,80,85,94,106,141,147,184],"vertex":[23,29,52,56,87,145],"u,":[24],"hole":[26,60],"v":[30,57,88],"and":[31,176,180],"obstacles":[32,65],"in":[33,116],"remaining":[35],"vertices":[36,108],"T.":[38],"By":[39],"an":[40],"mRJ":[41,110,127,152,171,187],"move":[42,77],"we":[43],"mean":[44],"moved":[49],"from":[50,82,100,134],"u":[53,83],"to":[54,84,104,118,125,139,143],"having":[58],"jumping":[62],"over":[63],"m":[64,71,162],"along":[66],"path.":[68],"The":[69],"case":[70],"=":[72],"0":[73],"simple":[76,119,150],"taking":[79],"adjacent":[86],"with":[89],"hole.":[91],"We":[92,173],"investigate":[93],"problem":[95],"moving":[97],"its":[101],"initial":[102],"position":[103],"all":[105],"other":[107],"using":[109,149],"moves":[111],"(for":[112],"some":[113],"fixed":[114],"m)":[115],"addition":[117],"moves.":[120,153],"A":[121,154],"said":[124],"be":[126],"reachable":[128,178,188],"if":[129],"exists":[131,166],"it":[136],"possible":[138],"take":[140],"any":[144],"or":[151],"connected":[155],"graph":[156],"1RJ":[158],"reachable.":[159,172],"However,":[160],"for":[161,183],"\u2265":[163],"2":[164],"graphs":[167],"are":[169],"not":[170],"characterize":[174],"2RJ":[175],"3RJ":[177],"trees":[179],"give":[181],"bound":[182],"diameter":[185],"trees.":[189]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"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"}