Abstract
Enumeration of rooted trees is a major area of research in computer science and mathematics. Rooted ordered trees are used to solve combinatorial optimization problems, analyze the structure of chemical compounds, and many others. Several researchers from different continents have given different algorithms for generating rooted ordered trees. Different encodings have been used to represent the rooted ordered trees by these researchers. We have introduced the children sequence to represent each rooted ordered tree. In this paper, our proposed algorithm, All-Ordered-Trees, uses an efficient algebraic approach to generate all the children sequences (representing rooted ordered trees) in lexicographic order for a given number of vertices, n. With slight modification, this algorithm can also be used to generate degree-bound rooted ordered trees. We have also implemented three existing algorithms in this domain and included the experimental results of these algorithms with the experimental results of our proposed algorithm for comparative study. From the experimental results, we observe that each tree can be generated in approximately constant time.
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Chakraborty, S., Bhattacharyya, R., Chakraborty, M., Pal, R.K. (2023). Generation of All Rooted Ordered Trees. In: Chaki, R., Chaki, N., Cortesi, A., Saeed, K. (eds) Applied Computing for Software and Smart Systems. ACSS 2023. Lecture Notes in Networks and Systems, vol 781. Springer, Singapore. https://doi.org/10.1007/978-981-99-7783-3_1
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