{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T09:22:01Z","timestamp":1778664121573,"version":"3.51.4"},"reference-count":30,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-0746673"],"award-info":[{"award-number":["CCF-0746673"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p>\n            A\n            <jats:italic>spanner<\/jats:italic>\n            of an undirected unweighted graph is a subgraph that approximates the distance metric of the original graph with some specified accuracy. Specifically, we say\n            <jats:italic>H<\/jats:italic>\n            \u2286\n            <jats:italic>G<\/jats:italic>\n            is an\n            <jats:italic>f<\/jats:italic>\n            -spanner of\n            <jats:italic>G<\/jats:italic>\n            if any two vertices\n            <jats:italic>u<\/jats:italic>\n            ,\n            <jats:italic>v<\/jats:italic>\n            at distance\n            <jats:italic>d<\/jats:italic>\n            in\n            <jats:italic>G<\/jats:italic>\n            are at distance at most\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>d<\/jats:italic>\n            ) in\n            <jats:italic>H<\/jats:italic>\n            . There is clearly some trade-off between the sparsity of\n            <jats:italic>H<\/jats:italic>\n            and the\n            <jats:italic>distortion<\/jats:italic>\n            function\n            <jats:italic>f<\/jats:italic>\n            , though the nature of the optimal trade-off is still poorly understood.\n          <\/jats:p>\n          <jats:p>\n            In this article we present a simple, modular framework for constructing sparse spanners that is based on interchangable components called\n            <jats:italic>connection schemes<\/jats:italic>\n            . By assembling connection schemes in different ways we can recreate the additive 2- and 6-spanners of Aingworth et al. [1999] and Baswana et al. [2009], and give spanners whose multiplicative distortion quickly tends toward 1. Our results rival the simplicity of all previous algorithms and provide substantial improvements (up to a doubly exponential reduction in edge density) over the comparable spanners of Elkin and Peleg [2004] and Thorup and Zwick [2006].\n          <\/jats:p>","DOI":"10.1145\/1644015.1644022","type":"journal-article","created":{"date-parts":[[2010,8,24]],"date-time":"2010-08-24T13:16:40Z","timestamp":1282655800000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":44,"title":["Low distortion spanners"],"prefix":"10.1145","volume":"6","author":[{"given":"Seth","family":"Pettie","sequence":"first","affiliation":[{"name":"University of Michigan, Ann Arbor, MI"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2009,12,28]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796303421"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02189308"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/4221.4227"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90017-9"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/0405013"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2006.29"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1868237.1868242"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.v30:4"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480103431046"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/050630696"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2000.1134"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgor.2003.08.001"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539797327908"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539701393384"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00446-005-0147-2"},{"key":"e_1_2_1_16_1","volume-title":"Theory of Graphs and its Applications","author":"Erd\u0151s P."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2004.04.011"},{"key":"e_1_2_1_18_1","doi-asserted-by":"crossref","unstructured":"Narasimhan G. and Smid M. 2007. Geometric Spanner Networks. Cambridge University Press.   Narasimhan G. and Smid M. 2007. Geometric Spanner Networks. 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