{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T23:19:05Z","timestamp":1773184745784,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2001,2,1]],"date-time":"2001-02-01T00:00:00Z","timestamp":980985600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[2001,2]]},"DOI":"10.1007\/bf02679621","type":"journal-article","created":{"date-parts":[[2007,7,29]],"date-time":"2007-07-29T00:42:49Z","timestamp":1185669769000},"page":"238-261","source":"Crossref","is-referenced-by-count":51,"title":["On the analysis of stochastic divide and conquer algorithms"],"prefix":"10.1007","volume":"29","author":[{"given":"U.","family":"R\u00f6sler","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02679621_CR1","doi-asserted-by":"crossref","unstructured":"Alsmeyer, G.Erneuerungstheorie. Teubner, 1991.","DOI":"10.1007\/978-3-663-09977-2"},{"key":"BF02679621_CR2","unstructured":"Bertram-Kretzberg, C. Analyse von Quicksort-Varianten. Diplomarbeit, Dortmund, 1991."},{"key":"BF02679621_CR3","first-page":"1196","volume":"9","author":"P.J. Bickel","year":"1981","unstructured":"Bickel, P.J., and Freedman, D.A. Some asymptotic theory for the bootstrap.Annals of Probability 9, 1196\u20131217, 1981.","journal-title":"Annals of Probability"},{"key":"BF02679621_CR4","volume-title":"Eine Methode zur asymptotischen Behandlung einer Klasse von Rekursionsgleichungen mit einer Anwendung in der stochastischen Analyse des Quicksort-Algorithmus","author":"V. Bruhn","year":"1996","unstructured":"Bruhn, V. Eine Methode zur asymptotischen Behandlung einer Klasse von Rekursionsgleichungen mit einer Anwendung in der stochastischen Analyse des Quicksort-Algorithmus. Dissertation, Christian-Albrechts-Universit\u00e4t zu Kiel, 1996."},{"key":"BF02679621_CR5","unstructured":"Dobrow, R.P., and Fill, J.A. Total path length for random recursive trees. Preprint to appear inCombinatorics, Probability & Computing."},{"key":"BF02679621_CR6","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1145\/362736.362753","volume":"13","author":"M.H. Emden van","year":"1970","unstructured":"van Emden, M.H. Increasing the efficiency of Quicksort.Communications of the Association or Computing Machinery 13, 563\u2013567, 1970.","journal-title":"Communications of the Association or Computing Machinery"},{"key":"BF02679621_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/3-540-55719-9_74","volume-title":"Analytic Analysis of Algorithms","author":"P. Flajolet","year":"1992","unstructured":"Flajolet, P.Analytic Analysis of Algorithms. Lecture Notes in Computer Science, vol. 623, pp. 186\u2013210, Ed. W. Kuich, Springer-Verlag, Berlin, 1992."},{"key":"BF02679621_CR8","doi-asserted-by":"crossref","first-page":"252","DOI":"10.2307\/1427920","volume":"28","author":"R. Gr\u00fcbel","year":"1996","unstructured":"Gr\u00fcbel, R., and R\u00f6sler, U. Asymptotic distribution theory for Hoare\u2019s selection algorithm.Advances in Applied Probability 28, 252\u2013269, 1996.","journal-title":"Advances in Applied Probability"},{"key":"BF02679621_CR9","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1051\/ita\/1989230303171","volume":"23","author":"P. Hennequin","year":"1989","unstructured":"Hennequin, P. Combinatorial analysis of Quicksort algorithm.Informatique th\u00e9orique et Applications\/Theoretical Informatics and Applications 23, 317\u2013333, 1989.","journal-title":"Informatique th\u00e9orique et Applications\/Theoretical Informatics and Applications"},{"key":"BF02679621_CR10","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1145\/366622.366644","volume":"4","author":"C.A.R. Hoare","year":"1961","unstructured":"Hoare, C.A.R. Algorithm 64: Quicksort.Communications of the Association for Computing Machinery 4, 321, 1961.","journal-title":"Communications of the Association for Computing Machinery"},{"key":"BF02679621_CR11","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1093\/comjnl\/5.1.10","volume":"5","author":"C.A.R. Hoare","year":"1962","unstructured":"Hoare, C.A.R. Quicksort.Computer Journal 5, 10\u201315, 1962.","journal-title":"Computer Journal"},{"key":"BF02679621_CR12","volume-title":"The Art of Computer Programming, Vol. 3","author":"D.E. Knuth","year":"1973","unstructured":"Knuth, D.E.The Art of Computer Programming, Vol. 3. Addison-Wesley, Reading, MA, 1973."},{"key":"BF02679621_CR13","unstructured":"McDiarmid, C., and Hayward, R. Strong concentration for Quicksort.Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 414\u2013421, 1992."},{"key":"BF02679621_CR14","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.2307\/3215021","volume":"34","author":"V. Paulsen","year":"1997","unstructured":"Paulsen, V. The moment of FIND.Journal of Applied Probability 34, 1079\u20131082, 1997.","journal-title":"Journal of Applied Probability"},{"key":"BF02679621_CR15","doi-asserted-by":"crossref","first-page":"770","DOI":"10.2307\/1428133","volume":"27","author":"S.T. Rachev","year":"1995","unstructured":"Rachev, S.T., and R\u00fcschendorf, L. Probability metrics and recursive algorithms.Advances in Applied Probability 27, 770\u2013799, 1995.","journal-title":"Advances in Applied Probability"},{"key":"BF02679621_CR16","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1051\/ita\/1991250100851","volume":"25","author":"U. R\u00f6sler","year":"1991","unstructured":"R\u00f6sler, U. A limit theorem for \u201cQuicksort\u201d.Informatique th\u00e9orique et Applications\/Theoretical Informatics and Applications 25, 85\u2013100, 1991.","journal-title":"Informatique th\u00e9orique et Applications\/Theoretical Informatics and Applications"},{"key":"BF02679621_CR17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/0304-4149(92)90035-O","volume":"42","author":"U. R\u00f6sler","year":"1992","unstructured":"R\u00f6sler, U. A fixed point theorem for distributions.Stochastic Processes and their Applications 42, 195\u2013214, 1992.","journal-title":"Stochastic Processes and their Applications"},{"key":"BF02679621_CR18","unstructured":"R\u00f6sler, U. The view backwards on the Algorithms FIND. Berichtsreihe des Mathematischen Seminars Kiel, Christian-Albrechts-Universit\u00e4t zu Kiel, www.numerik.uni-kiel\/reports\/ Bericht 99-?, 1998."},{"key":"BF02679621_CR19","unstructured":"R\u00f6sler, U. Orlicz norms for measures. Berichtsreihe des Mathematischen Seminars Kiel, Christian-Albrechts-Universit\u00e4t zu Kiel, www.numerik.uni-kiel\/reports\/ Bericht 99-?, 1998."},{"key":"BF02679621_CR20","doi-asserted-by":"crossref","unstructured":"R\u00f6sler, U., and R\u00fcschendorf, L. The contraction method for recursive algorithms.Algorithmica, this issue.","DOI":"10.1007\/BF02679611"},{"key":"BF02679621_CR21","doi-asserted-by":"crossref","unstructured":"Roura, S. An improved Master Theorem for divide-and-conquer recurrences.Proceedings of the 24th International Colloquium (ICALP-97), pp. 449\u2013459, 1997.","DOI":"10.1007\/3-540-63165-8_201"},{"key":"BF02679621_CR22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/BF00289467","volume":"7","author":"R. Sedgewick","year":"1977","unstructured":"Sedgewick, R. The analysis of Quicksort programs.Acta Informatica 7, 327\u2013355, 1977.","journal-title":"Acta Informatica"},{"key":"BF02679621_CR23","unstructured":"Sedgewick, R.Quicksort. Stanford Computer Science Report STAN-CS-75-492, Ph.D. thesis: 1975. Also published by Garland, New York. 1980."},{"key":"BF02679621_CR24","volume-title":"Algorithms","author":"R. Sedgewick","year":"1988","unstructured":"Sedgewick, R.Algorithms, Second edition. Addison-Wesley, Reading, MA, 1988.","edition":"Second edition"},{"key":"BF02679621_CR25","volume-title":"An Introduction to the Analysis of Algorithms","author":"R. Sedgewick","year":"1996","unstructured":"Sedgewick, R., and Flajolet, P.An Introduction to the Analysis of Algorithms. Addison-Wesley, Reading, MA, 1996."}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02679621.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02679621\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02679621","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T07:52:18Z","timestamp":1558338738000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02679621"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,2]]},"references-count":25,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2001,2]]}},"alternative-id":["BF02679621"],"URL":"https:\/\/doi.org\/10.1007\/bf02679621","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"value":"0178-4617","type":"print"},{"value":"1432-0541","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,2]]}}}