{"id":"https://openalex.org/W2569472613","doi":"https://doi.org/10.1137/140951382","title":"Cutting Corners Cheaply, or How to Remove Steiner Points","display_name":"Cutting Corners Cheaply, or How to Remove Steiner Points","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2569472613","doi":"https://doi.org/10.1137/140951382","mag":"2569472613"},"language":"en","primary_location":{"id":"doi:10.1137/140951382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140951382","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5018176999","display_name":"Lior Kamma","orcid":"https://orcid.org/0000-0002-2380-7195"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lior Kamma","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037378898","display_name":"Robert Krauthgamer","orcid":"https://orcid.org/0009-0003-8154-3735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Krauthgamer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102936404","display_name":"Huy L. Nguy\u00ean","orcid":"https://orcid.org/0000-0001-5128-6545"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huy L. Nguy\u1ec5n","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018176999"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8041,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.9145578,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"975","last_page":"995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8812721967697144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8165395259857178},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6443208456039429},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5259827971458435},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5245875716209412},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43243059515953064},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4231830835342407},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4216364622116089},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07871341705322266}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8812721967697144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165395259857178},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6443208456039429},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5259827971458435},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5245875716209412},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43243059515953064},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4231830835342407},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4216364622116089},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07871341705322266},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140951382","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140951382","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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":9,"referenced_works":["https://openalex.org/W1968729061","https://openalex.org/W1992849490","https://openalex.org/W1998544343","https://openalex.org/W2045446569","https://openalex.org/W2106663623","https://openalex.org/W2397920857","https://openalex.org/W2714858040","https://openalex.org/W3030774092","https://openalex.org/W4245082111"],"related_works":["https://openalex.org/W3086542228","https://openalex.org/W1985880617","https://openalex.org/W4377372033","https://openalex.org/W1626217631","https://openalex.org/W1991466591","https://openalex.org/W2962962718","https://openalex.org/W2921972394","https://openalex.org/W2951867195","https://openalex.org/W3157491188","https://openalex.org/W1853337082"],"abstract_inverted_index":{"Our":[0,92,101],"main":[1],"result":[2],"is":[3,54,59,111,135,169],"that":[4,37,58,67,114,130,160,201],"the":[5,21,74,149,158,167,179,194,199,203],"Steiner":[6],"point":[7],"removal":[8],"(SPR)":[9],"problem":[10],"can":[11],"always":[12],"be":[13],"solved":[14],"with":[15],"polylogarithmic":[16],"distortion,":[17],"which":[18,128],"answers":[19],"in":[20,32,79,82,163,178],"affirmative":[22],"a":[23,46,55,62,97,104,121,136,182],"question":[24],"posed":[25],"by":[26,207],"Chan,":[27],"Xia,":[28],"Konjevod,":[29],"and":[30,45,81],"Richa":[31],"2006.":[33],"Specifically,":[34],"we":[35],"prove":[36],"for":[38,68,124,131,153,185,215],"every":[39,69,115,132,154,186],"edge-weighted":[40],"graph":[41,56],"$G":[42],"=":[43],"(V,E,w)$":[44],"subset":[47],"of":[48,64,107,139,143,166,181,189,196,198],"terminals":[49,71],"$T":[50],"\\subseteq":[51],"V$,":[52],"there":[53,134],"$G'=(T,E',w')$":[57],"isomorphic":[60],"to":[61],"minor":[63],"$G$":[65,80],"such":[66],"two":[70],"$u,v\\in":[72],"T$,":[73],"shortest-path":[75,187],"distances":[76],"between":[77],"them":[78],"$G'$":[83],"satisfy":[84],"$d_{G,w}(u,v)":[85],"\\le":[86,88,213],"d_{G',w'}(u,v)":[87],"O(\\log^5|T|)":[89],"\\cdot":[90],"d_{G,w}(u,v)$.":[91],"existence":[93],"proof":[94,102],"actually":[95],"gives":[96],"randomized":[98,137],"polynomial-time":[99],"algorithm.":[100],"features":[103],"new":[105],"variant":[106],"metric":[108,117],"decomposition.":[109],"It":[110],"well":[112],"known":[113],"finite":[116],"space":[118],"$(X,d)$":[119],"admits":[120],"$\\beta$-separating":[122],"decomposition":[123],"$\\beta=O(\\log":[125],"\\lvert":[126],"X\\rvert)$,":[127],"means":[129],"$\\Delta>0$":[133],"partitioning":[138],"$X$":[140],"into":[141],"clusters":[142,165,197],"diameter":[144],"at":[145,170],"most":[146,171],"$\\Delta$,":[147],"satisfying":[148],"following":[150],"separation":[151],"property:":[152],"$x,y":[155],"\\in":[156],"X$,":[157],"probability":[159],"they":[161],"lie":[162],"different":[164],"partition":[168,200],"$\\beta\\,d(x,y)/\\Delta$.":[172],"We":[173],"introduce":[174],"an":[175],"additional":[176],"requirement":[177],"form":[180],"tail":[183],"bound:":[184],"$P$":[188],"length":[190],"$d(P)":[191],"\\leq":[192],"\\Delta/\\beta$,":[193],"number":[195],"meet":[202],"path":[204],"$P$,":[205],"denoted":[206],"$Z_P$,":[208],"satisfies":[209],"$\\Pr[Z_P":[210],">":[211],"t]":[212],"2e^{-\\Omega(t)}$":[214],"all":[216],"$t>0$.":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
