{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:03Z","timestamp":1750308123159,"version":"3.41.0"},"reference-count":4,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[1980,2,1]],"date-time":"1980-02-01T00:00:00Z","timestamp":318211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1980,2]]},"abstract":"<jats:p>An algorithm of Khachian type for deciding the consistency of m \u2265 2 linear equalities with integer coefficients is described. New iteration formulas for updating the center and the matrix that define each localizing ellipsoid are given. A much sharper bound than that in [1] and [2] for the radius of the initial sphere is given. The new bound depends on the dimension of the solution space, but does &lt;u&gt;not&lt;\/u&gt; depend explicitly on m. The algorithm is much faster than Khachian's original algorithm. The volume reduction factor in the new algorithm is, in a sense, optimal. Results of computer experiments on the symbolic mathematical system MACSYMA are included.<\/jats:p>","DOI":"10.1145\/1089212.1089214","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"8-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["MACSYMA experiments with a modified Khachian-type algorithm in linear programming"],"prefix":"10.1145","volume":"14","author":[{"given":"Ned","family":"Anderson","sequence":"first","affiliation":[{"name":"Kent State University, Kent, OH"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul S.","family":"Wang","sequence":"additional","affiliation":[{"name":"Kent State University, Kent, OH"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1980,2]]},"reference":[{"key":"e_1_2_1_2_1","unstructured":"L. G. Khachian \"A Polynomial Algorithm in Linear Programming\" Soviet Math. Dokl. Vol. 20(1979) No. 1.  L. G. Khachian \"A Polynomial Algorithm in Linear Programming\" Soviet Math. Dokl. Vol. 20(1979) No. 1."},{"key":"e_1_2_1_3_1","volume-title":"O. Shisha","author":"Klee V.","year":"1972","unstructured":"V. Klee and G. J. Minty , \" How Good is the Simplex Algorithm? \", Inequalities III, ed. O. Shisha , Academic Press , N.Y. , 1972 . V. Klee and G. J. Minty, \"How Good is the Simplex Algorithm?\", Inequalities III, ed. O. Shisha, Academic Press, N.Y., 1972."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.206.4418.545"},{"key":"e_1_2_1_5_1","volume-title":"Version 9","author":"Mathlab Group","year":"1977","unstructured":"Mathlab Group , MACSYMA REFERENCE MANUAL , Version 9 , MIT , 1977 . Mathlab Group, MACSYMA REFERENCE MANUAL, Version 9, MIT, 1977."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089212.1089214","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089212.1089214","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:22Z","timestamp":1750262902000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089212.1089214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1980,2]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1980,2]]}},"alternative-id":["10.1145\/1089212.1089214"],"URL":"https:\/\/doi.org\/10.1145\/1089212.1089214","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1980,2]]},"assertion":[{"value":"1980-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}