{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T07:56:42Z","timestamp":1790495802274,"version":"4.1.0"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>The celebrated semidefinite programming algorithm for MAX CUT introduced by Goemans and Williamson was known to have a performance ratio of at least $\\alpha=\\frac 2 {\\pi} \\min_{0 &lt; \\theta\\le \\pi} \\frac \\theta {1-\\cos \\theta}$ ($0.87856 &lt; \\alpha &lt; 0.87857$); the exact performance ratio was unknown. We prove that the performance ratio of their algorithm is exactly $\\alpha$. Furthermore, we show that it is impossible to add valid linear constraints to improve the performance ratio.<\/jats:p>","DOI":"10.1137\/s0097539797321481","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"336-350","source":"Crossref","is-referenced-by-count":46,"title":["How Good is the Goemans--Williamson MAX CUT Algorithm?"],"prefix":"10.1137","volume":"29","author":[{"given":"Howard","family":"Karloff","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02592023"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0134012"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04295-9"},{"key":"R4","unstructured":"U. Feige and M. X. Goemans,\n                      Approximating the value of two\u2010prover proof systems, with applications to MAX 2SAT and MAX DICUT\n                      , in Proceedings, Third Israel Symposium on the Theory of Computing and Systems, Tel\u2010Aviv, Israel, 1995."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1145\/227683.227684"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1145\/274787.274791"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Howard Karloff, How good is the Goemans\u2010Williamson MAX CUT algorithm? ACM, New York, 1996, 427\u20134341427540","DOI":"10.1145\/237814.237990"},{"key":"R8","unstructured":"D. Knuth,\n                      Combinatorial Matrices\n                      , Notes, Institut Mittag\u2010Leffler, 1991, revised 1993."}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539797321481","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:49Z","timestamp":1787336089000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539797321481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S0097539797321481"],"URL":"https:\/\/doi.org\/10.1137\/s0097539797321481","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}