{"id":"https://openalex.org/W7128638588","doi":"https://doi.org/10.1109/focs63196.2025.00014","title":"Almost Tight Additive Guarantees for k-Edge-Connectivity","display_name":"Almost Tight Additive Guarantees for k-Edge-Connectivity","publication_year":2025,"publication_date":"2025-12-14","ids":{"openalex":"https://openalex.org/W7128638588","doi":"https://doi.org/10.1109/focs63196.2025.00014"},"language":null,"primary_location":{"id":"doi:10.1109/focs63196.2025.00014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs63196.2025.00014","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 66th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5122062860","display_name":"Nikhil Kumar","orcid":null},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nikhil Kumar","raw_affiliation_strings":["Combinatorics and Optimization (C & O) Tata Institute of Fundamental Research Mumbai,India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Combinatorics and Optimization (C & O) Tata Institute of Fundamental Research Mumbai,India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031968426","display_name":"Chaitanya Swamy","orcid":"https://orcid.org/0000-0003-1108-7941"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chaitanya Swamy","raw_affiliation_strings":["University of Waterloo,Waterloo,Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo,Waterloo,Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.7026244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"205","last_page":"219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9314000010490417,"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":0.9314000010490417,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.023099999874830246,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.019600000232458115,"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/multigraph","display_name":"Multigraph","score":0.7440999746322632},{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"Vertex connectivity","score":0.6162999868392944},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.6146000027656555},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5162000060081482},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.4772999882698059},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.4677000045776367},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.4456999897956848},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4415999948978424},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4207000136375427}],"concepts":[{"id":"https://openalex.org/C17758045","wikidata":"https://www.wikidata.org/wiki/Q2642629","display_name":"Multigraph","level":3,"score":0.7440999746322632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6822999715805054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6771000027656555},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.6162999868392944},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.6146000027656555},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.4772999882698059},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.4456999897956848},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4415999948978424},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4207000136375427},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.41019999980926514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3928000032901764},{"id":"https://openalex.org/C131992880","wikidata":"https://www.wikidata.org/wiki/Q2528185","display_name":"Subgraph isomorphism problem","level":3,"score":0.3799000084400177},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.36500000953674316},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.2840000092983246},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.260699987411499},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/focs63196.2025.00014","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs63196.2025.00014","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 66th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,26,78,99,103,111,120,148,164,196,212,235,273,290,301,319,324,333,336,339,345,348,366,372],"$\\boldsymbol{k}$-edge":[3],"connected":[4,70,81,93,183,237],"spanning":[5,238],"subgraph":[6,33,71,82,94,184],"(k-ECSS)":[7],"problem,":[8,241],"where":[9,179,242,335],"we":[10,60,88,180,253,281],"are":[11,140,323,351],"given":[12],"an":[13,176,246,312,354],"undirected":[14],"graph":[15],"$G=(V,":[16],"E)$":[17],"with":[18,192,222,311],"nonnegative":[19],"edge":[20,40,92,194,218,227,247],"costs":[21,219],"$\\left\\{c_{e}\\right\\}_{e":[22],"\\in":[23],"E}$,":[24],"and":[25,154,163,168,261,278,286,296,304,347],"goal":[27],"is":[28,38,127,342],"to":[29,200,272,299],"find":[30],"a":[31,62,68,90,223,255,363],"minimum-cost":[32],"H":[34],"of":[35,53,72,77,83,95,105,119,134,151,160,166,185,245,276,315,332,338,374],"G":[36],"that":[37,66,76],"k":[39,47],"connected,":[41],"i.e.,":[42],"there":[43],"exist":[44],"at":[45,74,97,187,343,371],"least":[46],"edge-disjoint":[48],"paths":[49],"between":[50],"every":[51],"pair":[52],"vertices":[54],"in":[55,158,226,365,377],"H.":[56],"For":[57,251],"even":[58,259],"k,":[59,87,260],"present":[61],"polynomial":[63],"time":[64],"algorithm":[65,167,257,264],"computes":[67],"($k-2$)-edge":[69],"cost":[73,96,104,186,197,303,337],"most":[75,98,188,344],"optimal":[79,112],"k-edge":[80,236],"G;":[84],"for":[85,123,131,216,234,258,265,294,307,318,327],"odd":[86,266],"obtain":[89,181,254],"$(k-3)$":[91],"optimum.":[100],"In":[101],"fact,":[102],"our":[106,138,172,269],"solution":[107,161,340],"does":[108],"not":[109],"exceed":[110],"value,":[113],"$\\mathbf{L":[114],"P}_{\\boldsymbol{k}":[115],"\\text":[116,206],"{-ECSSLP":[117,207],"}}^{\\boldsymbol{*}}$":[118],"natural":[121],"LP-relaxation":[122],"$\\boldsymbol{k}$-ECSS.":[124],"Since":[125],"k-ECSS":[126,277,295],"$A":[128],"P":[129],"X$-hard":[130],"all":[132],"values":[133],"$k":[135],"\\geq":[136],"2$,":[137],"results":[139,233,293,326],"nearly":[141],"optimal.":[142],"They":[143],"also":[144,174,231,282],"significantly":[145],"improve":[146],"upon":[147,211],"recent":[149],"work":[150],"Hershkowitz,":[152],"Klein,":[153],"Zenklusen":[155],"[1],":[156],"both":[157],"terms":[159],"quality":[162],"simplicity":[165],"its":[169],"analysis.":[170],"Interestingly,":[171],"techniques":[173,270],"yield":[175,300],"alternate":[177],"guarantee,":[178],"a($k-1$)-edge":[182],"$1.5":[189],"\\cdot":[190],"\\mathrm{LP}_{\\boldsymbol{k}-\\mathrm{ECSSLP}}^{*}$;":[191],"unit":[193,217,224],"costs,":[195],"guarantee":[198,215],"improves":[199,210],"$\\left(1+\\frac{4}{3":[201],"k}\\right)":[202],"\\cdot$":[203],"LP":[204],"$_{\\boldsymbol{k}":[205],"}}^{\\boldsymbol{*}}$,":[208],"which":[209],"state-of-the-art":[213],"approximation":[214,263],"[2],":[220],"albeit":[221],"loss":[225],"connectivity.":[228],"Our":[229,292],"k-ECSS-result":[230],"yields":[232],"multigraph":[239],"(k-ECSM)":[240],"multiple":[243],"copies":[244],"can":[248],"be":[249],"selected.":[250],"$\\boldsymbol{k}$-ECSM,":[252],"$\\left(1+\\frac{2}{k}\\right)$-approximation":[256],"$\\mathbf{a}\\left(1+\\frac{3}{k}\\right)$":[262],"$\\boldsymbol{k}$.":[267],"Finally,":[268],"extend":[271,298],"degree-bounded":[274,309,328],"versions":[275,310],"k-ECSM,":[279],"wherein":[280],"impose":[283],"degree":[284,320],"lower-":[285],"upper-":[287],"bounds":[288],"on":[289],"nodes.":[291],"k-ECSM":[297,330],"same":[302],"connectivity":[305,349],"guarantees":[306],"these":[308],"additive":[313,355],"violation":[314],"(roughly)":[316],"2":[317],"bounds.":[321],"These":[322],"first":[325],"$\\{k$-ECSS,":[329],"$\\}$":[331],"form":[334],"obtained":[341],"optimum,":[346],"constraints":[350],"violated":[352],"by":[353,379],"constant.":[356],"Work":[357],"done":[358],"while":[359],"N.":[360],"Kumar":[361],"was":[362],"postdoc":[364],"$C":[367],"\\&":[368],"O$":[369],"department":[370],"University":[373],"Waterloo.":[375],"Supported":[376],"part":[378],"C.":[380],"Swamy\u2019s":[381],"NSERC":[382],"Discovery":[383],"grant.":[384]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2026-02-12T00:00:00"}