{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T09:05:41Z","timestamp":1655283941208},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2018,8,14]],"date-time":"2018-08-14T00:00:00Z","timestamp":1534204800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p>We give combinatorial descriptions of two stochastic growth models for series-parallel networks introduced by Hosam Mahmoud by encoding the growth process via recursive tree structures. Using decompositions of the tree structures and applying analytic combinatorics methods allows a study of quantities in the corresponding series-parallel networks. For both models we obtain limiting distribution results for the degree of the poles and the length of a random source-to-sink path, and furthermore we get asymptotic results for the expected number of source-to-sink paths. Moreover, we introduce generalizations of these stochastic models by encoding the growth process of the networks via further important increasing tree structures.<\/jats:p>","DOI":"10.1017\/s096354831800038x","type":"journal-article","created":{"date-parts":[[2018,8,14]],"date-time":"2018-08-14T04:14:35Z","timestamp":1534220075000},"page":"574-599","source":"Crossref","is-referenced-by-count":1,"title":["Combinatorial Analysis of Growth Models for Series-Parallel Networks"],"prefix":"10.1017","volume":"28","author":[{"given":"MARKUS","family":"KUBA","sequence":"first","affiliation":[]},{"given":"ALOIS","family":"PANHOLZER","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,14]]},"reference":[{"key":"S096354831800038X_ref17","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1214\/14-AOP919","article-title":"On a functional contraction method","volume":"43","author":"Neininger","year":"2015","journal-title":"Ann. Probab."},{"key":"S096354831800038X_ref15","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0304-3975(94)00308-6","article-title":"Probabilistic analysis of bucket recursive trees","volume":"144","author":"Mahmoud","year":"1995","journal-title":"Theoret. Comput. Sci."},{"key":"S096354831800038X_ref14","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1017\/S0269964814000138","article-title":"Some properties of binary series-parallel graphs","volume":"28","author":"Mahmoud","year":"2014","journal-title":"Probab. Engng Inform. Sci."},{"key":"S096354831800038X_ref10","doi-asserted-by":"crossref","first-page":"3255","DOI":"10.1016\/j.tcs.2010.05.030","article-title":"A combinatorial approach to the analysis of bucket recursive trees","volume":"411","author":"Kuba","year":"2010","journal-title":"Theoret. Comput. Sci."},{"key":"S096354831800038X_ref9","doi-asserted-by":"publisher","DOI":"10.1214\/10-PS160"},{"key":"S096354831800038X_ref16","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1214\/aoap\/1075828056","article-title":"A general limit theorem for recursive algorithms and combinatorial structures","volume":"14","author":"Neininger","year":"2004","journal-title":"Ann. Appl. Probab."},{"key":"S096354831800038X_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"S096354831800038X_ref6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1002\/rsa.20290","article-title":"Vertices of given degree in series-parallel graphs","volume":"36","author":"Drmota","year":"2010","journal-title":"Random Struct. Alg."},{"key":"S096354831800038X_ref8","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.10030"},{"key":"S096354831800038X_ref4","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1017\/S0963548399003855","article-title":"Total path length for random recursive trees","volume":"8","author":"Dobrow","year":"1999","journal-title":"Combin. Probab. Comput."},{"key":"S096354831800038X_ref18","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/S0304-3975(02)00729-6","article-title":"Analysis of multiple quickselect variants","volume":"302","author":"Panholzer","year":"2003","journal-title":"Theoret. Comput. Sci."},{"key":"S096354831800038X_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719796"},{"key":"S096354831800038X_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-015-0941-9"},{"key":"S096354831800038X_ref20","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20161"},{"key":"S096354831800038X_ref13","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1017\/S026996481300003X","article-title":"Some node degree properties of series-parallel graphs evolving under a stochastic growth model","volume":"27","author":"Mahmoud","year":"2013","journal-title":"Probab. Engng Inform. Sci."},{"key":"S096354831800038X_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-49529-2_16"},{"key":"S096354831800038X_ref19","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/rsa.20027","article-title":"The distribution of the size of the ancestor-tree and of the induced spanning subtree for random trees","volume":"25","author":"Panholzer","year":"2004","journal-title":"Random Struct. Alg."},{"key":"S096354831800038X_ref12","volume-title":"P\u00f3lya Urn Models","author":"Mahmoud","year":"2009"},{"key":"S096354831800038X_ref11","volume-title":"Probability Theory I","author":"Lo\u00e8ve","year":"1977"},{"key":"S096354831800038X_ref3","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1002\/rsa.20428","article-title":"Psi-series method for equality of random trees and quadratic convolution recurrences","volume":"44","author":"Chern","year":"2014","journal-title":"Random Struct. Alg."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096354831800038X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T05:19:37Z","timestamp":1564031977000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096354831800038X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,14]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["S096354831800038X"],"URL":"https:\/\/doi.org\/10.1017\/s096354831800038x","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,14]]}}}