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We also give a polynomial-time algorithm for the following related problem: Given a molecular formula, select, uniformly at random, a structural isomer having the given formula.<\/jats:p>","DOI":"10.1137\/s0097539797318864","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"834-853","source":"Crossref","is-referenced-by-count":4,"title":["Randomly Sampling Molecules"],"prefix":"10.1137","volume":"29","author":[{"given":"Leslie Ann","family":"Goldberg","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark","family":"Jerrum","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(78)90059-6"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-2670(95)00291-7"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-26.2.201"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(83)80039-0"},{"key":"R5","unstructured":"B. Bollob\u00e1s,\n                      Random Graphs\n                      , Academic Press, New York, London, 1985."},{"key":"R6","unstructured":"N. G. de Bruijn,\n                      P\u00f3lya\u2019s theory of counting\n                      , in Applied Combinatorial Mathematics, E. F. Beckenbach, ed., John Wiley & Sons, Inc., New York, 1964;"},{"key":"R6","unstructured":"see especially section 5.13."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(83)90021-4"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1021\/ci00008a013"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1021\/ci00021a031"},{"key":"R10","unstructured":"J. L. Faulon,\n                      private communication\n                      , Sandia National Laboratories, Albuquerque, NM, 1995."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90226-7"},{"key":"R12","unstructured":"P. Flajolet, P. Zimmerman, and B. Van Cutsem,\n                      A calculus for the random generation of unlabelled combinatorial structures\n                      , in preparation."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(90)90164-D"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90029-E"},{"key":"R15","unstructured":"Meena Mahajan, P. Subramanya, V. Vinay, A combinatorial algorithm for Pfaffians, Lecture Notes in Comput. Sci., Vol. 1627, Springer, Berlin, 1999, 134\u20131431730329"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4664-0"},{"key":"R17","unstructured":"Ronald Read, Some recent results in chemical enumeration, Springer, Berlin, 1972, 0\u20130, 243\u2013259. Lecture Notes in Math., Vol. 30349:4800"},{"key":"R18","unstructured":"R. C. Read,\n                      The enumeration of acyclic chemical compounds\n                      , in Chemical Applications of Graph Theory, A. T. Balaban, ed., Academic Press, New York, London, 1976."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.2307\/2308012"},{"key":"R20","volume-title":"Logic: a foundation for computer science","author":"Sperschneider V.","year":"1991"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1021\/ci9502663"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(81)90021-3"},{"key":"R23","unstructured":"N. C. Wormald,\n                      Some Problems in the Enumeration of Labelled Graphs\n                      , Ph.D. thesis, Department of Mathematics, University of Newcastle, New South Wales, Australia, 1978."},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80021-4"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0216048"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(91)90401-M"}],"container-title":["SIAM Journal on Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0097539797318864","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:14:34Z","timestamp":1787336074000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0097539797318864"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S0097539797318864"],"URL":"https:\/\/doi.org\/10.1137\/s0097539797318864","relation":{},"ISSN":["0097-5397","1095-7111"],"issn-type":[{"value":"0097-5397","type":"print"},{"value":"1095-7111","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}