{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:23:59Z","timestamp":1759335839934},"reference-count":23,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4120,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Tutte\u2010Gr\u00f6thendieck polynomial <jats:italic>T<\/jats:italic>(<jats:italic>G<\/jats:italic>; <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>) of a graph <jats:italic>G<\/jats:italic> encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (<jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>) plane give the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper <jats:italic>k<\/jats:italic>\u2010colorings, the (all terminal) reliability probability of the graph, and various other invariants the exact computation of each of which is well known to be #<jats:italic>P<\/jats:italic>\u2010hard. Here we develop a general technique that supplies fully polynomial randomised approximation schemes for approximating the value of <jats:italic>T<\/jats:italic>(<jats:italic>G<\/jats:italic>; <jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>) for any dense graph <jats:italic>G<\/jats:italic>, that is, any graph on <jats:italic>n<\/jats:italic> vertices whose minimum.<\/jats:p>","DOI":"10.1002\/rsa.3240060409","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:50:39Z","timestamp":1180205439000},"page":"459-478","source":"Crossref","is-referenced-by-count":30,"title":["Polynomial time randomized approximation schemes for Tutte\u2013Gr\u00f6thendieck invariants: The dense case"],"prefix":"10.1002","volume":"6","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[]},{"given":"Alan","family":"Frieze","sequence":"additional","affiliation":[]},{"given":"Dominic","family":"Welsh","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Probabilistic Method","author":"Alon N.","year":"1991"},{"key":"e_1_2_1_3_2","article-title":"A randomised approximation algorithm for counting the number of forests in dense graphs","author":"Annan J. 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