{"id":"https://openalex.org/W2083866643","doi":"https://doi.org/10.1145/1400863.1400877","title":"Symmetric range assignment with disjoint MST constraints","display_name":"Symmetric range assignment with disjoint MST constraints","publication_year":2008,"publication_date":"2008-08-18","ids":{"openalex":"https://openalex.org/W2083866643","doi":"https://doi.org/10.1145/1400863.1400877","mag":"2083866643"},"language":"en","primary_location":{"id":"doi:10.1145/1400863.1400877","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1400863.1400877","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fifth international workshop on Foundations of mobile computing","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/A5048043622","display_name":"Eric Schmutz","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eric Schmutz","raw_affiliation_strings":["Drexel University, Philadelphia, PA, USA","Drexel University, Philadelphia, PA, USA;"],"affiliations":[{"raw_affiliation_string":"Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Drexel University, Philadelphia, PA, USA;","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5048043622"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09067946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"65","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9984999895095825,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8608388900756836},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7086370587348938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6281009316444397},{"id":"https://openalex.org/keywords/unit-square","display_name":"Unit square","score":0.551415205001831},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5359474420547485},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5007519721984863},{"id":"https://openalex.org/keywords/assignment-problem","display_name":"Assignment problem","score":0.4741223156452179},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.46988633275032043},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46197569370269775},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.44616997241973877},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4390961527824402},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42479178309440613},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08355408906936646}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8608388900756836},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7086370587348938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6281009316444397},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.551415205001831},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5359474420547485},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5007519721984863},{"id":"https://openalex.org/C85044808","wikidata":"https://www.wikidata.org/wiki/Q620614","display_name":"Assignment problem","level":2,"score":0.4741223156452179},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.46988633275032043},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46197569370269775},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.44616997241973877},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4390961527824402},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42479178309440613},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08355408906936646},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1400863.1400877","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1400863.1400877","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fifth international workshop on Foundations of mobile computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.664.2330","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.664.2330","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.drexel.edu/%7Eeschmutz/PAPERS/smallj.pdf?origin%3Dpublication_detail","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W173428383","https://openalex.org/W1522185922","https://openalex.org/W1551519020","https://openalex.org/W1965964249","https://openalex.org/W1991951594","https://openalex.org/W1996075091","https://openalex.org/W2002245803","https://openalex.org/W2015610066","https://openalex.org/W2054861138","https://openalex.org/W2059772103","https://openalex.org/W2088273596","https://openalex.org/W2088839217","https://openalex.org/W2106841911","https://openalex.org/W2109384905","https://openalex.org/W2124608963","https://openalex.org/W2134137046","https://openalex.org/W2162229660","https://openalex.org/W2163575832","https://openalex.org/W2169293240"],"related_works":["https://openalex.org/W4256429076","https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W2348092930","https://openalex.org/W2012063272","https://openalex.org/W3129272755","https://openalex.org/W1654151311","https://openalex.org/W2138685729","https://openalex.org/W4321438198","https://openalex.org/W1993553799"],"abstract_inverted_index":{"If":[0],"V":[1,17],"is":[2,20,40,53,110],"a":[3,33],"set":[4],"of":[5,23,106],"n":[6,97],"points":[7,99],"in":[8,100],"the":[9,48,71,76,85,103,107],"unit":[10],"square":[11],"[0,":[12,101],"1]2,":[13,102],"and":[14,45,64],"if":[15,44,47],"R:":[16],"\u2192":[18],"\u211c+":[19],"an":[21,41],"assignment":[22,73],"positive":[24],"real":[25],"numbers":[26],"(radii)":[27],"to":[28,29,58,84],"those":[30],"points,":[31],"define":[32],"graph":[34],"G(R)":[35,88],"as":[36],"follows:":[37],"{v,":[38],"w}":[39],"undirected":[42],"edge":[43],"only":[46],"Euclidean":[49],"dis-tance":[50],"d(v,":[51],"w)":[52],"less":[54],"than":[55],"or":[56],"equal":[57],"min(R(v),R(w)).":[59],"Given":[60],"\u03b1":[61],"\u2265":[62],"1":[63],"k":[65,92],"\u2208":[66],"Z+,":[67],"let":[68],"R\u2217k":[69],"be":[70],"range":[72],"that":[74,87],"minimizes":[75],"function":[77],"J(R)":[78],"=":[79],"P":[80],"v\u2208V":[81],"R(v)\u03b1,":[82],"subject":[83],"constraint":[86],"has":[89],"at":[90],"least":[91],"edge-disjoint":[93],"spanning":[94],"trees.":[95],"For":[96],"random":[98],"expected":[104],"value":[105],"optimum,":[108],"E(J(R\u2217k)),":[109],"asymptotically":[111],"\u0398(n":[112]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
