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Journal articles on the topic 'Generating trees'

Author: Grafiati

Published: 25 June 2021

Last updated: 11 March 2023

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1

Banderier, Cyril, Mireille Bousquet-Mélou, Alain Denise, Philippe Flajolet, Danièle Gardy, and Dominique Gouyou-Beauchamps. "Generating functions for generating trees." Discrete Mathematics 246, no. 1-3 (March 2002): 29–55. http://dx.doi.org/10.1016/s0012-365x(01)00250-3.

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2

Skarbek, Wladyslaw. "Generating ordered trees." Theoretical Computer Science 57, no. 1 (April 1988): 153–59. http://dx.doi.org/10.1016/0304-3975(88)90169-7.

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3

Mlinarić, Danijel, Vedran Mornar, and Boris Milašinović. "Generating Trees for Comparison." Computers 9, no. 2 (April 29, 2020): 35. http://dx.doi.org/10.3390/computers9020035.

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Tree comparisons are used in various areas with various statistical or dissimilarity measures. Given that data in various domains are diverse, and a particular comparison approach could be more appropriate for specific applications, there is a need to evaluate different comparison approaches. As gathering real data is often an extensive task, using generated trees provides a faster evaluation of the proposed solutions. This paper presents three algorithms for generating random trees: parametrized by tree size, shape based on the node distribution and the amount of difference between generated trees. The motivation for the algorithms came from unordered trees that are created from class hierarchies in object-oriented programs. The presented algorithms are evaluated by statistical and dissimilarity measures to observe stability, behavior, and impact on node distribution. The results in the case of dissimilarity measures evaluation show that the algorithms are suitable for tree comparison.

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4

Pikhurko, Oleg. "Generating Edge-Labeled Trees." American Mathematical Monthly 112, no. 10 (December 1, 2005): 919. http://dx.doi.org/10.2307/30037632.

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5

Pallo, J. "Generating trees withnnodes andmleaves." International Journal of Computer Mathematics 21, no. 2 (January 1987): 133–44. http://dx.doi.org/10.1080/00207168708803562.

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6

Pikhurko, Oleg. "Generating Edge-Labeled Trees." American Mathematical Monthly 112, no. 10 (December 2005): 919–21. http://dx.doi.org/10.1080/00029890.2005.11920268.

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7

Sibun, Penelope. "GENERATING TEXT WITHOUT TREES." Computational Intelligence 8, no. 1 (February 1992): 102–22. http://dx.doi.org/10.1111/j.1467-8640.1992.tb00340.x.

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8

West, J. "Generating trees and forbidden subsequences." Discrete Mathematics 157, no. 1-3 (October 1, 1996): 271–83. http://dx.doi.org/10.1016/0012-365x(95)00271-w.

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9

Ruskey, Frank, and Andrzej Proskurowski. "Generating binary trees by transpositions." Journal of Algorithms 11, no. 1 (March 1990): 68–84. http://dx.doi.org/10.1016/0196-6774(90)90030-i.

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10

Atkinson, M. D., and J. R. Sack. "Generating binary trees at random." Information Processing Letters 41, no. 1 (January 1992): 21–23. http://dx.doi.org/10.1016/0020-0190(92)90075-7.

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11

West, Julian. "Generating trees and forbidden subsequences." Discrete Mathematics 157, no. 1-3 (October 1996): 363–74. http://dx.doi.org/10.1016/s0012-365x(96)83023-8.

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12

Zerling, David. "Generating binary trees using rotations." Journal of the ACM 32, no. 3 (July 1985): 694–701. http://dx.doi.org/10.1145/3828.214141.

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13

Parkinson, Hannah, Shaun Cole, and John Helly. "Generating dark matter halo merger trees." Monthly Notices of the Royal Astronomical Society 383, no. 2 (December 10, 2007): 557–64. http://dx.doi.org/10.1111/j.1365-2966.2007.12517.x.

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14

Sawada, Joe. "Generating rooted and free plane trees." ACM Transactions on Algorithms 2, no. 1 (January 2006): 1–13. http://dx.doi.org/10.1145/1125994.1125995.

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15

Mäkinen, Erkki. "Generating random binary trees — A survey." Information Sciences 115, no. 1-4 (April 1999): 123–36. http://dx.doi.org/10.1016/s0020-0255(98)10080-4.

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16

Johnsen, Ben. "Generating binary trees with uniform probability." BIT 31, no. 1 (March 1991): 15–31. http://dx.doi.org/10.1007/bf01952779.

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17

Korsh, James F. "Counting and randomly generating binary trees." Information Processing Letters 45, no. 6 (April 1993): 291–94. http://dx.doi.org/10.1016/0020-0190(93)90039-c.

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18

Merlini, Donatella, and M. Cecilia Verri. "Generating trees and proper Riordan Arrays." Discrete Mathematics 218, no. 1-3 (May 2000): 167–83. http://dx.doi.org/10.1016/s0012-365x(99)00343-x.

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19

Theiling, Henrik. "Generating Decision Trees for Decoding Binaries." ACM SIGPLAN Notices 36, no. 8 (August 2001): 112–20. http://dx.doi.org/10.1145/384196.384213.

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20

Xiang, L. "Generating Regular k-ary Trees Efficiently." Computer Journal 43, no. 4 (April 1, 2000): 290–300. http://dx.doi.org/10.1093/comjnl/43.4.290.

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21

Venkatesh, S., and K. Balasubramanian. "Some Results on Generating Graceful Trees." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 570. http://dx.doi.org/10.14419/ijet.v7i4.10.21283.

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Let and be any two simple graphs. Then is the graph obtained by merging a vertex of each copy of with every attachment vertices of . Let be the one vertex union of copies of the given caterpillar with the common vertex as one of the penultimate vertices. If is any caterpillar, then define . Recursively for , construct ,that is, Here the tree considered for attachment with is a caterpillar, but not necessarily the same among the levels. In this paper we prove that the tree is graceful for

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22

Lee, C. C., D. T. Lee, and C. K. Wong. "Generating binary trees of bounded height." Acta Informatica 23, no. 5 (September 1986): 529–44. http://dx.doi.org/10.1007/bf00288468.

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23

Czabarka, É., P. L. Erdős, V. Johnson, and V. Moulton. "Generating functions for multi-labeled trees." Discrete Applied Mathematics 161, no. 1-2 (January 2013): 107–17. http://dx.doi.org/10.1016/j.dam.2012.08.010.

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24

Baccherini, D., D. Merlini, and R. Sprugnoli. "Level generating trees and proper Riordan arrays." Applicable Analysis and Discrete Mathematics 2, no. 1 (2008): 69–91. http://dx.doi.org/10.2298/aadm0801069b.

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25

Nguyen, Dai Hai, and Koji Tsuda. "Generating reaction trees with cascaded variational autoencoders." Journal of Chemical Physics 156, no. 4 (January 28, 2022): 044117. http://dx.doi.org/10.1063/5.0076749.

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26

Elizalde, Sergi. "Generating Trees for Permutations Avoiding Generalized Patterns." Annals of Combinatorics 11, no. 3-4 (December 2007): 435–58. http://dx.doi.org/10.1007/s00026-007-0328-8.

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27

van Baronaigien, D. Roelants, and Frank Ruskey. "Generating t-ary trees in A-order." Information Processing Letters 27, no. 4 (April 1988): 205–13. http://dx.doi.org/10.1016/0020-0190(88)90027-0.

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28

Xiang, Limin, Kazuo Ushijima, and Changjie Tang. "On generating -ary trees in computer representation." Information Processing Letters 77, no. 5-6 (March 2001): 231–38. http://dx.doi.org/10.1016/s0020-0190(00)00155-1.

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29

Breslin, C., and M. J. F. Gales. "Directed decision trees for generating complementary systems." Speech Communication 51, no. 3 (March 2009): 284–95. http://dx.doi.org/10.1016/j.specom.2008.09.004.

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30

Vatter, Vincent. "Finitely labeled generating trees and restricted permutations." Journal of Symbolic Computation 41, no. 5 (May 2006): 559–72. http://dx.doi.org/10.1016/j.jsc.2005.10.003.

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31

Noonan, Robert E. "An algorithm for generating abstract syntax trees." Computer Languages 10, no. 3-4 (January 1985): 225–36. http://dx.doi.org/10.1016/0096-0551(85)90018-9.

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32

Høyland, Kjetil, and Stein W. Wallace. "Generating Scenario Trees for Multistage Decision Problems." Management Science 47, no. 2 (February 2001): 295–307. http://dx.doi.org/10.1287/mnsc.47.2.295.9834.

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33

Li, Chuan, Oliver Deussen, Yi-Zhe Song, Phil Willis, and Peter Hall. "Modeling and generating moving trees from video." ACM Transactions on Graphics 30, no. 6 (December 2011): 1–12. http://dx.doi.org/10.1145/2070781.2024161.

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34

Korsh, J. F. "Generating T-ary Trees in Linked Representation." Computer Journal 48, no. 4 (May 3, 2005): 488–97. http://dx.doi.org/10.1093/comjnl/bxh110.

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35

VAJNOVSZKI, VINCENT, and CHRIS PHILLIPS. "SYSTOLIC GENERATION OF k-ARY TREES." Parallel Processing Letters 09, no. 01 (March 1999): 93–101. http://dx.doi.org/10.1142/s0129626499000116.

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The only parallel generating algorithms for k-ary trees are those of Akl and Stojmenović in 1996 and of Vajnovszki and Phillips in 1997. In the first of them, trees are represented by an inversion table and the processor model is a linear aray multicomputer. In the second, trees are represented by bitstrings and the algorithm executes on a shared memory multiprocessor. In this paper we give a parallel generating algorithm for k-ary trees represented by generalized P–sequences for execution on a linear array multicomputer.

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36

Uadilova, A. D. "Generating functions for ternary algebras and ternary trees." Russian Mathematics 54, no. 8 (July 1, 2010): 57–66. http://dx.doi.org/10.3103/s1066369x10080086.

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37

Kuba, Markus. "Generating Functions of Embedded Trees and Lattice Paths." Fundamenta Informaticae 117, no. 1-4 (2012): 215–27. http://dx.doi.org/10.3233/fi-2012-697.

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38

Anđelić, Milica, and Dejan Živković. "Efficient Algorithm for Generating Maximal L-Reflexive Trees." Symmetry 12, no. 5 (May 13, 2020): 809. http://dx.doi.org/10.3390/sym12050809.

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The line graph of a graph G is another graph of which the vertex set corresponds to the edge set of G, and two vertices of the line graph of G are adjacent if the corresponding edges in G share a common vertex. A graph is reflexive if the second-largest eigenvalue of its adjacency matrix is no greater than 2. Reflexive graphs give combinatorial ground to generate two classes of algebraic numbers, Salem and Pisot numbers. The difficult question of identifying those graphs whose line graphs are reflexive (called L-reflexive graphs) is naturally attacked by first answering this question for trees. Even then, however, an elegant full characterization of reflexive line graphs of trees has proved to be quite formidable. In this paper, we present an efficient algorithm for the exhaustive generation of maximal L-reflexive trees.

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39

Lafrance, Philip, Ortrud R. Oellermann, and Timothy Pressey. "Generating and Enumerating Digitally Convex Sets of Trees." Graphs and Combinatorics 32, no. 2 (July 16, 2015): 721–32. http://dx.doi.org/10.1007/s00373-015-1604-8.

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40

West, Julian. "Generating trees and the Catalan and Schröder numbers." Discrete Mathematics 146, no. 1-3 (November 1995): 247–62. http://dx.doi.org/10.1016/0012-365x(94)00067-1.

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41

Pallo, Jean M. "A simple algorithm for generating neuronal dendritic trees." Computer Methods and Programs in Biomedicine 33, no. 3 (November 1990): 165–69. http://dx.doi.org/10.1016/0169-2607(90)90038-b.

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42

Bazhenov, N. A. "Boolean Algebras with Distinguished Endomorphisms and Generating Trees." Journal of Mathematical Sciences 215, no. 4 (April 27, 2016): 460–74. http://dx.doi.org/10.1007/s10958-016-2851-9.

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43

Merlini, Donatella. "Proper generating trees and their internal path length." Discrete Applied Mathematics 156, no. 5 (March 2008): 627–46. http://dx.doi.org/10.1016/j.dam.2007.08.051.

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44

Bostan, Alin, and Antonio Jiménez-Pastor. "On the exponential generating function of labelled trees." Comptes Rendus. Mathématique 358, no. 9-10 (January 5, 2021): 1005–9. http://dx.doi.org/10.5802/crmath.108.

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45

Setiono, R., and Huan Liu. "A connectionist approach to generating oblique decision trees." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 29, no. 3 (June 1999): 440–44. http://dx.doi.org/10.1109/3477.764880.

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46

Sethuraman, G., and V. Murugan. "Generating Graceful Trees from Caterpillars by Recursive Attachment." Electronic Notes in Discrete Mathematics 53 (September 2016): 133–47. http://dx.doi.org/10.1016/j.endm.2016.05.012.

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47

Porter, Adam A., and Richard W. Selby. "Evaluating techniques for generating metric-based classification trees." Journal of Systems and Software 12, no. 3 (July 1990): 209–18. http://dx.doi.org/10.1016/0164-1212(90)90041-j.

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48

Yadav, M., P. Khan, A. K. Singh, and B. Lohani. "GENERATING GIS DATABASE OF STREET TREES USING MOBILE LIDAR DATA." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-5 (November 15, 2018): 233–37. http://dx.doi.org/10.5194/isprs-annals-iv-5-233-2018.

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<p><strong>Abstract.</strong> Mobile LiDAR captures complete details of street trees located along roadway and it is most efficient tool for executing large scale projects for road side trees mapping. Information of road-side trees locations and their morphological characteristics are essential for road widening project planning, road safety and autonomous vehicles. We propose a method to generate GIS database of street trees using information of automatically extracted street trees using mobile LiDAR data. Proposed method first organizes mobile LiDAR input data in partially overlapping cylinders and then morphological characteristics of tree crown and trunk, respectively are used to detect trees falling within cylinders. Finally complete tree structure point cloud is recovered from cylinder by vertical cylinders fitting to crown and trunk separately. The proposed method is tested on point cloud data acquired by StreetMapper 360 of 57<span class="thinspace"></span>m long roadway. Completeness and correctness of 88.24% and 93.75% respectively are obtained in test site.</p>

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49

STEEL, M. A., and L. A. SZÉKELY. "Teasing Apart Two Trees." Combinatorics, Probability and Computing 16, no. 6 (November 2007): 903–22. http://dx.doi.org/10.1017/s0963548307008656.

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A widely studied model for generating binary sequences is to ‘evolve’ them on a tree according to a symmetric Markov process. We show that under this model distinguishing the true (model) tree from a false one is substantially ‘easier’ (in terms of the sequence length needed) than determining the true tree. The key tool is a new and near-tight Ramsey-type result for binary trees.

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50

Kubicka, Ewa. "An Efficient Method of Examining all Trees." Combinatorics, Probability and Computing 5, no. 4 (December 1996): 403–13. http://dx.doi.org/10.1017/s0963548300002157.

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In this paper, we present a techique for examining all trees of a given order. Our approach is based on the Beyer and Hedetniemi algorithm for generating all rooted trees of a given order and on the Wright, Richmond, Odlyzko and McKay algorithm for generating all free trees of a given order. In the introduction we describe these algorithms. We also give a precise evaluation of the average number of moves it takes to generate a rooted tree, which improves the upper bound given by Beyer and Hedetniemi. In the second section we present a new method of examining all trees which uses these generating algorithms. The last section contains two applications of the method introduced. The main result of the paper is that the average number of steps required by the proposed algorithm to examine a rooted tree is bounded by a constant independent of the order of a tree.

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