{"id":"https://openalex.org/W2031536548","doi":"https://doi.org/10.1137/050630696","title":"Sparse Sourcewise and Pairwise Distance Preservers","display_name":"Sparse Sourcewise and Pairwise Distance Preservers","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2031536548","doi":"https://doi.org/10.1137/050630696","mag":"2031536548"},"language":"en","primary_location":{"id":"doi:10.1137/050630696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630696","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5067588072","display_name":"Don Coppersmith","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Don Coppersmith","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075683085","display_name":"Michael Elkin","orcid":"https://orcid.org/0000-0003-4257-2122"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Elkin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067588072"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9155,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.85608132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"20","issue":"2","first_page":"463","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11797","display_name":"graph theory and CDMA systems","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9919000267982483,"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/T12288","display_name":"Optimization and Search Problems","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8683059215545654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8514963388442993},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7904492616653442},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6979809403419495},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.597275972366333},{"id":"https://openalex.org/keywords/ultrametric-space","display_name":"Ultrametric space","score":0.5369771122932434},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4951237738132477},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4558611512184143},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.45384472608566284},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.41091370582580566},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.12221622467041016},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.059647560119628906},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.04920947551727295}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8683059215545654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8514963388442993},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7904492616653442},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6979809403419495},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.597275972366333},{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.5369771122932434},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4951237738132477},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4558611512184143},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.45384472608566284},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.41091370582580566},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.12221622467041016},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.059647560119628906},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.04920947551727295}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050630696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630696","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W163991090","https://openalex.org/W1981859328","https://openalex.org/W2005580106","https://openalex.org/W2028697609","https://openalex.org/W2050306584","https://openalex.org/W2063491776","https://openalex.org/W2075459377","https://openalex.org/W2091569826","https://openalex.org/W2167816765","https://openalex.org/W2979473749","https://openalex.org/W4232548171","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W4287598215","https://openalex.org/W3105794585","https://openalex.org/W4236333616","https://openalex.org/W2999666600","https://openalex.org/W4245978557","https://openalex.org/W4285726363","https://openalex.org/W4288563602","https://openalex.org/W2462375376","https://openalex.org/W2019622749","https://openalex.org/W1641703864"],"abstract_inverted_index":{"We":[0,95,198],"introduce":[1],"and":[2,8,19,106,168,209,218],"study":[3,224],"the":[4,71,156,164,175,201,204,223,229],"notions":[5],"of":[6,23,25,39,61,66,73,81,88,110,115,117,125,138,149,163,187,192,206,215,225,231],"pairwise":[7,37,64,123],"sourcewise":[9,86,147],"preservers.":[10],"Given":[11],"an":[12],"undirected":[13,100],"N-vertex":[14,103],"graph":[15,104],"G":[16,40,67,89,105,126,150],"=":[17,29,53,77,112,140],"(V,E)":[18],"a":[20,36,56,63,85,121,145],"set":[21,57,72,108],"P":[22,44,76,109,111],"pairs":[24,75,114],"vertices,":[26],"let":[27],"G'":[28],"(V,H),":[30],"H":[31],"\\subseteq":[32,59,136],"E,":[33],"be":[34,171,220],"called":[35,84],"preserver":[38,65,87,124,148],"with":[41,68,90,127,151,194],"respect":[42,69,91,128,152],"to":[43,70,92,129,153,179],"if":[45],"for":[46,98,132],"every":[47,99,107,133],"pair":[48],"{u,w}":[49],"\\in":[50],"P,":[51],"distG'(u,w)":[52],"distG(u,w).":[54],"For":[55],"S":[58,93,135,139],"V":[60,137],"sources,":[62,142],"all":[74],"(S":[78],"\\atop":[79],"2)":[80],"sources":[82],"is":[83,177,214],".":[94],"prove":[96],"that":[97,161,200,211],"possibly":[101],"weighted":[102],"O(N1/2)":[113],"vertices":[116],"G,":[118],"there":[119,143],"exists":[120,144],"linear-size":[122,146],"P.":[130],"Consequently,":[131],"subset":[134],"O(N1/4)":[141],"S.":[154],"On":[155],"negative":[157],"side":[158],"we":[159,212],"show":[160],"neither":[162],"two":[165],"exponents":[166],"(1/2":[167],"1/4)":[169],"can":[170],"improved":[172],"even":[173],"when":[174],"attention":[176],"restricted":[178],"unweighted":[180],"graphs.":[181],"Our":[182],"lower":[183],"bounds":[184],"involve":[185],"constructions":[186],"dense":[188],"convexly":[189],"independent":[190,216],"sets":[191],"vectors":[193],"small":[195],"Euclidean":[196],"norms.":[197],"believe":[199],"link":[202],"between":[203],"areas":[205],"discrete":[207],"geometry":[208],"spanners":[210],"establish":[213],"interest":[217],"might":[219],"useful":[221],"in":[222,228],"other":[226],"problems":[227],"area":[230],"low-distortion":[232],"embeddings.":[233]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}