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Generating rooted and free plane trees

Author:

Joe SawadaAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 2, Issue 1

Pages 1 - 13

https://doi.org/10.1145/1125994.1125995

Published: 01 January 2006 Publication History

Abstract

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.

References

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Beyer, T., and Hedetniemi, S. M. 1980. Constant time generation of rooted trees. SIAM J. Comput. 9, 706--712.

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Cattell, K., Ruskey, F., Sawada, J., Serra, M., and Miers, C. R. 2000. Fast algorithms to generate necklaces, unlabeled necklaces, and irreducible polynomials over gf(2). J. Alg. 37, 2, 267--282.

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deBruijn, N. G., and Morselt, B. 1967. A note on plane trees. J. Combinat. Theory 2, 27--34.

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Mallows, C. L., and Wachter, K. W. 1972. Valency enumeration of rooted plane trees. J. Austral. Math. Soc. 13, 472--476.

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Nakano, S. 2002. Efficient generation of plane trees. Inf. Proc. Lett. 84, 167--172.

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Ruskey, F., and Sawada, J. 1999. An efficient algorithm for generating necklaces of fixed density. SIAM J. Comput. 29, 671--684.

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Sawada, J. 2002. A fast algorithm for generating non-isomorphic chord diagrams. SIAM J. Disc. Math. 15, 4, 546--561.

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Cited By

Chakraborty SChakraborty MPal R(2024)Generation of all rooted trees up to a given heightInnovations in Systems and Software Engineering10.1007/s11334-022-00467-120:3(467-475)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s11334-022-00467-1
Chakraborty SBhattacharyya RChakraborty MPal R(2023)Generation of All Rooted Ordered TreesApplied Computing for Software and Smart Systems10.1007/978-981-99-7783-3_1(3-19)Online publication date: 27-Dec-2023
https://doi.org/10.1007/978-981-99-7783-3_1
Varrette SKieffer EPinel F(2022)Optimizing the Resource and Job Management System of an Academic HPC & Research Computing Facility2022 21st International Symposium on Parallel and Distributed Computing (ISPDC)10.1109/ISPDC55340.2022.00027(129-137)Online publication date: Jul-2022
https://doi.org/10.1109/ISPDC55340.2022.00027
Show More Cited By

Index Terms

Generating rooted and free plane trees
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 2, Issue 1

January 2006

134 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1125994

Issue’s Table of Contents

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 January 2006

Published in TALG Volume 2, Issue 1

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Cited By

Chakraborty SChakraborty MPal R(2024)Generation of all rooted trees up to a given heightInnovations in Systems and Software Engineering10.1007/s11334-022-00467-120:3(467-475)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s11334-022-00467-1
Chakraborty SBhattacharyya RChakraborty MPal R(2023)Generation of All Rooted Ordered TreesApplied Computing for Software and Smart Systems10.1007/978-981-99-7783-3_1(3-19)Online publication date: 27-Dec-2023
https://doi.org/10.1007/978-981-99-7783-3_1
Varrette SKieffer EPinel F(2022)Optimizing the Resource and Job Management System of an Academic HPC & Research Computing Facility2022 21st International Symposium on Parallel and Distributed Computing (ISPDC)10.1109/ISPDC55340.2022.00027(129-137)Online publication date: Jul-2022
https://doi.org/10.1109/ISPDC55340.2022.00027
Parque V(2022)Learning Obstacle-Avoiding Lattice Paths using Swarm Heuristics: Exploring the Bijection to Ordered Trees2022 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC55065.2022.9870344(1-8)Online publication date: 18-Jul-2022
https://dl.acm.org/doi/10.1109/CEC55065.2022.9870344
Parque VMiyashita T(2021)An Efficient Scheme for the Generation of Ordered Trees in Constant Amortized Time2021 15th International Conference on Ubiquitous Information Management and Communication (IMCOM)10.1109/IMCOM51814.2021.9377349(1-8)Online publication date: 4-Jan-2021
https://doi.org/10.1109/IMCOM51814.2021.9377349
Hoppe TPetrone A(2019)Integer sequence discovery from small graphsDiscrete Applied Mathematics10.1016/j.dam.2015.07.017201:C(172-181)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.dam.2015.07.017
Mohammadi SNowzari-Dalini A(2017)A parallel algorithm for generation of RNA secondary structures with length n and k base-pairsIran Journal of Computer Science10.1007/s42044-017-0001-21:1(11-17)Online publication date: 24-Oct-2017
https://doi.org/10.1007/s42044-017-0001-2
ISHIKAWA MYAMANAKA KOTACHI YNAKANO S(2012)Enumerating All Rooted Trees Including k LeavesIEICE Transactions on Information and Systems10.1587/transinf.E95.D.763E95-D:3(763-768)Online publication date: 2012
https://doi.org/10.1587/transinf.E95.D.763
Yamanaka KOtachi YNakano S(2012)Efficient enumeration of ordered trees with k leavesTheoretical Computer Science10.1016/j.tcs.2011.01.017442(22-27)Online publication date: Jul-2012
https://doi.org/10.1016/j.tcs.2011.01.017
Yamanaka KOtachi YNakano S(2009)Efficient Enumeration of Ordered Trees with k Leaves (Extended Abstract)Proceedings of the 3rd International Workshop on Algorithms and Computation10.1007/978-3-642-00202-1_13(141-150)Online publication date: 18-Feb-2009
https://dl.acm.org/doi/10.1007/978-3-642-00202-1_13
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