{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:46:40Z","timestamp":1787320000572,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[1989,2]]},"abstract":"<jats:p>Where S is a set of N points in the unit square, let $t(S)$ be the Euclidean length of the shortest traveling salesman tour through S. Let $t_N = \\max_st (S)$. We improve Few\u2019s bound [Mathematika, 2 (1955), pp. 141\u2013144] that $t_N \\leqq \\sqrt {2N} + 7\/4$ to $t_N \\leqq \\alpha \\sqrt N + 11$, where $\\alpha \/\\sqrt 2 &lt; 0.984$.<\/jats:p>","DOI":"10.1137\/0402010","type":"journal-article","created":{"date-parts":[[2005,2,23]],"date-time":"2005-02-23T05:58:14Z","timestamp":1109138294000},"page":"91-99","source":"Crossref","is-referenced-by-count":33,"title":["How Long Can a Euclidean Traveling Salesman Tour Be?"],"prefix":"10.1137","volume":"2","author":[{"given":"Howard J.","family":"Karloff","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,8]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"M. Bern, Two probabilistic results on rectilinear Steiner trees, Proc. 18th Annual ACM Symposium on the Theory of Computing, Berkeley, CA, 1986, 433\u2013441","DOI":"10.1145\/12130.12175"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100034095"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00149359"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300000784"},{"key":"R5","series-title":"Wiley-Intersci. Ser. Discrete Math.","first-page":"181","volume-title":"The traveling salesman problem","author":"Karp R. M.","year":"1985"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(84)90067-4"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0212009"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1951-0045403-1"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0402010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T12:54:36Z","timestamp":1787316876000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0402010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,2]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1989,2]]}},"alternative-id":["10.1137\/0402010"],"URL":"https:\/\/doi.org\/10.1137\/0402010","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,2]]}}}