{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:40:37Z","timestamp":1750308037245,"version":"3.41.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"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":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>This article has two main results. First, we develop a simple algorithm to list all nonisomorphic rooted plane trees in lexicographic order using a level sequence representation. Then, by selecting a unique centroid to act as the root of a free plane tree, we apply the rooted plane tree algorithm to develop an algorithm to list all nonisomorphic free plane trees. The latter algorithm also uses a level sequence representation and lists all free plane trees with a unique centroid first followed by all free plane trees with two centroids. Both algorithms are proved to run in constant amortized time using straightforward bounding methods.<\/jats:p>","DOI":"10.1145\/1125994.1125995","type":"journal-article","created":{"date-parts":[[2006,5,8]],"date-time":"2006-05-08T16:09:20Z","timestamp":1147104560000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Generating rooted and free plane trees"],"prefix":"10.1145","volume":"2","author":[{"given":"Joe","family":"Sawada","sequence":"first","affiliation":[{"name":"University of Guelph, Guelph, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,1]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/0209055"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2000.1108"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(67)80111-X"},{"key":"e_1_2_1_4_1","volume-title":"G","author":"DiBattista G. D.","year":"1998","unstructured":"DiBattista , G. D. , Eades , P. , Tamassia , R. , and Tollis , I . G 1998 . Graph Drawing. Prentice-Hall , Englewood Cliffs, NJ. DiBattista, G. D., Eades, P., Tamassia, R., and Tollis, I. G 1998. Graph Drawing. Prentice-Hall, Englewood Cliffs, NJ."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(64)50038-4"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1869.70.185"},{"volume-title":"Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM","author":"Li G.","key":"e_1_2_1_7_1","unstructured":"Li , G. and Ruskey , F . 1999. Advantages of forward thinking in generating rooted and free trees . In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM , New York, S939--S940. Li, G. and Ruskey, F. 1999. Advantages of forward thinking in generating rooted and free trees. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, S939--S940."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700009228"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(02)00240-5"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539798344112"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480100377970"},{"key":"e_1_2_1_12_1","first-page":"43","article-title":"Placing trees in lexicographic order","volume":"3","author":"Scoins H.","year":"1967","unstructured":"Scoins , H. 1967 . Placing trees in lexicographic order . Mach. Intell. 3 , 43 -- 60 . Scoins, H. 1967. Placing trees in lexicographic order. Mach. Intell. 3, 43--60.","journal-title":"Mach. Intell."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73086-6_12"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300005659"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0215039"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1125994.1125995","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1125994.1125995","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:14:17Z","timestamp":1750259657000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1125994.1125995"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1145\/1125994.1125995"],"URL":"https:\/\/doi.org\/10.1145\/1125994.1125995","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2006,1]]},"assertion":[{"value":"2006-01-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}