{"id":"https://openalex.org/W2082352769","doi":"https://doi.org/10.1137/s0895480103431046","title":"Sparse Distance Preservers and Additive Spanners","display_name":"Sparse Distance Preservers and Additive Spanners","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2082352769","doi":"https://doi.org/10.1137/s0895480103431046","mag":"2082352769"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480103431046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103431046","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/A5109915650","display_name":"B\u00e9la Bollob\u00e1s","orcid":"https://orcid.org/0000-0002-9819-7213"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"B\u00e9la Bollob\u00e1s","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067588072","display_name":"Don Coppersmith","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"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":3,"corresponding_author_ids":["https://openalex.org/A5109915650"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7027,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.71251505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"4","first_page":"1029","last_page":"1055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9112070798873901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8265988826751709},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.6922613382339478},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6038736701011658},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5858593583106995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44024717807769775},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04912182688713074}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9112070798873901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8265988826751709},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.6922613382339478},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6038736701011658},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5858593583106995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44024717807769775},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04912182688713074},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480103431046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103431046","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":11,"referenced_works":["https://openalex.org/W1972978715","https://openalex.org/W1987996179","https://openalex.org/W2002041206","https://openalex.org/W2018963243","https://openalex.org/W2031874971","https://openalex.org/W2042333226","https://openalex.org/W2075459377","https://openalex.org/W2075862701","https://openalex.org/W4232548171","https://openalex.org/W4237496336","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W4287882779","https://openalex.org/W2046896701","https://openalex.org/W2265849288","https://openalex.org/W2140169421","https://openalex.org/W1996632063","https://openalex.org/W1981643426","https://openalex.org/W4378505325"],"abstract_inverted_index":{"For":[0],"an":[1],"unweighted":[2],"graph":[3,24,75,105,158],"$G":[4],"=":[5,8,19,99],"(V,E)$,":[6],"$G'":[7,18],"(V,E')$":[9],"is":[10,21,46,77,181],"a":[11,22,74,78,109,141,163,185,212,226],"subgraph":[12,68,79,110],"if":[13,25,85,138],"$E'":[14],"\\subseteq":[15,27],"E$,":[16],"and":[17,29,119,123,177,239],"(V',E',\\omega)$":[20],"Steiner":[23,70,129,143],"$V":[26],"V'$,":[28],"for":[30,86,125,156,251],"any":[31,104,127,157,252],"pair":[32,88],"of":[33,64,73,83,89,203,207,214,232,242],"vertices":[34,90,208],"$u,w":[35,91],"\\in":[36,92],"V$,":[37],"the":[38,49,62],"distance":[39,50,65,192,213],"between":[40,51,205],"them":[41,52],"in":[42,53],"$G'$":[43,72],"(denoted":[44,55],"$d_{G'}(u,w)$)":[45],"at":[47,113,211,215],"least":[48,216],"G":[54,76,84],"$d_G(u,w)$).":[56],"In":[57],"this":[58,179],"paper":[59],"we":[60,135,153],"introduce":[61],"notion":[63],"preserver.":[66],"A":[67],"(resp.,":[69,80,106,117],"graph)":[71],"Steiner)":[81],"D-preserver":[82,111,130,165],"every":[87],"V$":[93],"with":[94,112,166,230],"$d_G(u,w)":[95],"\\ge":[96],"D$,":[97],"$d_{G'}(u,w)":[98],"d_G(u,w)$.":[100],"We":[101,188,221],"show":[102,136,154,222],"that":[103,137,155,178,195,199,209,223,240],"digraph)":[107],"has":[108],"most":[114],"$O(n^2/D)$":[115],"edges":[116],"arcs),":[118],"there":[120,161,224],"are":[121,196,210,249],"graphs":[122],"digraphs":[124],"which":[126],"undirected":[128],"contains":[131],"$\\Omega(n^2/D)$":[132],"edges.":[133],"However,":[134],"one":[139,218],"allows":[140],"directed":[142],"(diSteiner)":[144],"D-preserver,":[145],"then":[146],"these":[147],"bounds":[148],"can":[149],"be":[150],"improved.":[151],"Specifically,":[152],"or":[159],"digraph":[160],"exists":[162,225],"diSteiner":[164],"$O({{n^2":[167],"\\cdot":[168,173],"\\log":[169,174,247],"D}":[170],"\\over":[171,235,245],"{D":[172],"n}})$":[175],"arcs,":[176],"result":[180],"tight":[182],"up":[183],"to":[184],"constant":[186],"factor.":[187],"also":[189],"study":[190],"D-preserving":[191,227,253],"labeling":[193,197,228,254],"schemes,":[194],"schemes":[198],"guarantee":[200],"precise":[201],"calculation":[202],"distances":[204],"pairs":[206],"D":[217],"from":[219],"another.":[220],"scheme":[229],"labels":[231,241],"size":[233,243],"$O({{n}":[234],"{D}}":[236,246],"\\log^2":[237],"n)$,":[238],"$\\Omega({{n}":[244],"D)$":[248],"required":[250],"scheme.":[255]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}