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Efficient loopless generation of Gray codes for -ary trees

Limin Xiang, Kazuo Ushijima, Changjie Tang
2000 Information Processing Letters  
Lett. 70 (1999) 7] to generate Gray codes for k-ary trees.  ...  Based on the algorithm, Gray codes for k-ary trees with n internal nodes (n 2 and k > 3) can be generated in at least 2 2(n−1) different ways easily.  ...  Acknowledgements The authors are very grateful to anonymous referees whose careful review improved the quality of the paper to a great extent.  ... 
doi:10.1016/s0020-0190(00)00139-3 fatcat:glrgl73aobb4dninzhkoyoacgi

On generating -ary trees in computer representation

Limin Xiang, Kazuo Ushijima, Changjie Tang
2001 Information Processing Letters  
Two new algorithms are presented in this paper to generate k-ary trees in computer representation.  ...  Many algorithms have been developed to generate sequences for trees, and a few are to generate trees themselves, i.e., in computer representation.  ...  In this paper, from Zaks' sequences [26] (a kind of well-formed integer sequences for k-ary trees) and Williamson's loopless algorithm [20] , a recursive and a loopless algorithm are presented for generating  ... 
doi:10.1016/s0020-0190(00)00155-1 fatcat:okvhfad3grg73dpjhtjsdlvxpq

Ranking and unranking algorithms for loopless generation of t-ary trees

A. Ahmadi-Adl, A. Nowzari-Dalini, H. Ahrabian
2010 Logic Journal of the IGPL  
These algorithms are designed based on a loopless generation algorithm which is given for z-sequences corresponding to t-ary trees by Roelants van Baronaigien and Xiang et al.  ...  Up to our knowledge no other ranking and unranking algorithms are given for Gray-codes corresponding to t-ary trees. The time complexity of both algorithms for t-ary trees with n nodes is O(n 2 t).  ...  Acknowledgements This research was partially supported by University of Tehran.  ... 
doi:10.1093/jigpal/jzp097 fatcat:danpotj6i5dpbdbv3s4o2t7edy

A Ranking Algorithm of Non-Regular Trees in Gray-Code Order

Ro–Yu Wu, Jou–Ming Chang, An–Hang Chen
2012 International Journal of Machine Learning and Computing  
Recently, Wu et al. (2010) introduced a concise representation called RD-sequences to represent all non-regular trees and proposed a loopless algorithm for generating all non-regular trees in a Gray-code  ...  A non-regular tree T with a prescribed branching sequence is an ordered tree whose internal nodes are numbered from 1 to n in preorder such that every node in T has a prescribed number of children.  ...  Many algorithms have been developed for generating regular trees including binary trees and k-ary trees.  ... 
doi:10.7763/ijmlc.2012.v2.233 fatcat:bfjnt5r7xfhjrmtekxlop5gxte

Cool-lex order and k-ary Catalan structures

Stephane Durocher, Pak Ching Li, Debajyoti Mondal, Frank Ruskey, Aaron Williams
2012 Journal of Discrete Algorithms  
For any given k, the sequence of k-ary Catalan numbers, C t,k = 1 kt+1 kt t , enumerates a number of combinatorial objects, including k-ary Dyck words of length n = kt and k-ary trees with t internal nodes  ...  The algorithms are also efficient in terms of memory, with the k-ary Dyck word algorithm using O(1) additional index variables, and the k-ary tree algorithm using O(t) additional pointers and index variables  ...  Generating k-ary trees Now we provide a loopless algorithm for generating k-ary trees with t internal nodes.  ... 
doi:10.1016/j.jda.2012.04.015 fatcat:gngocv35n5dglg5izigifkh3iu

Page 8406 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Mach. 20 (1973), 500-513; MR 51 #2335], algorithms have been described for loopless generation of binary trees, k-ary trees, and trees of mixed arity.  ...  , PA) Towers, beads, and loopless generation of trees with specified degrees.  ... 

Page 6211 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
Csaba Fabian (Bucharest) 95j:68066 68Q20 68P05 Korsh, James F. (1-TMPL-C; Philadelphia, PA) Loopless generation of k-ary tree sequences. (English summary) Inform. Process.  ...  This paper generalizes the rotation to k-ary trees and uses it to generate k-ary tree representations with constant time between them.” 95j:68067 68Q20 52C05 68Q25 Lempel, Mody (IL-TECH-C; Haifa); Paz,  ... 

Page 1215 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
general, loopless and simple outer maps are not trees.  ...  1215 sequence {f(n,k): 0<k <n} is unimodal with the maximum occurring at either |log,(”)| or |log,(m)| — 1. The authors note that the unimodality of f(n,k) was shown ear- lier by A. Odlyzko and L. B.  ... 

An explicit universal cycle for the (n-1)-permutations of ann-set

Frank Ruskey, Aaron Williams
2010 ACM Transactions on Algorithms  
Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be loopless.  ...  Finally, our Hamilton cycle can be used to construct an explicit universal cycle for the (n − 1)-permutations of a n-set, or as the basis of an efficient algorithm for generating every n-permutation of  ...  Acknowledgement The authors wish to thank the referee for carefully reading the paper and making a number of useful suggestions regarding the presentation.  ... 
doi:10.1145/1798596.1798598 fatcat:qikpwwhibjh2vfy6pcjqho6sgi

Generating Gray Codes in O(1) Worst-Case Time per Word [chapter]

Timothy Walsh
2003 Lecture Notes in Computer Science  
method of generating each word in a time bounded by a constant works under the additional condition that in the interval of words with the same prefix or suffix the next letter assumes at least two values  ...  the various concepts of minimality.  ...  A loopless algorithm for the k-ary generalization of the Bultena-Ruskey Gray code was obtained by D. Roelants van Baronaigien [19] .  ... 
doi:10.1007/3-540-45066-1_5 fatcat:o3louf4ysrepbgmpxagrvdkvhe

Model-based Sketching and Recovery with Expanders [chapter]

Bubacarr Bah, Luca Baldassarre, Volkan Cevher
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
For the tree and group-based sparsity models we describe in this paper, such projections can be obtained in linear time.  ...  The main computational cost of our algorithm depends on the difficulty of projecting onto the model-sparse set.  ...  Given a D-ary tree T (D ≥ 2), the k-tree sparse model T k is the collection of all possible k-rooted connected subtrees of T . A set S ⊆ [N ] is k-tree sparse (i.e.  ... 
doi:10.1137/1.9781611973402.112 dblp:conf/soda/BahBC14 fatcat:3h65pyybfnfnznvrugaxwldwem

A Gray Code for the Ideals of a Forest Poset

Y. Koda, F. Ruskey
1993 Journal of Algorithms  
This algorithm has the property that the amount of computation between successive ideals is O(1); such algorithms are said to be loopless.  ...  We present two algorithms for listing all ideals of a forest poset. These algorithms generate ideals in a Gray Code manner; that is, consecutive ideals di er by exactly one element.  ...  If all m i = k ? 1, then the product space consists of all k-ary strings, and if m i = i, then the product space can be regarded as the set of inversion vectors of all p! permutations.  ... 
doi:10.1006/jagm.1993.1044 fatcat:xwunyyhq25erncl5aoc7mmfwke

An explicit universal cycle for the (n-1)-permutations of an n-set [article]

Frank Ruskey, Aaron Williams
2007 arXiv   pre-print
Moreover, the algorithm produces each successive edge of the cycle in constant time; such algorithms are said to be loopless.  ...  The existence of such cycles was shown by Jackson (Discrete Mathematics, 149 (1996) 123-129) but the proof only shows that a certain directed graph is Eulerian, and Knuth (Volume 4 Fascicle 2, Generating  ...  An interesting case in point is the well-known De Bruijn cycle, which is a length k n circular string over a k-ary alphabet with the property that every length n string occurs as a substring.  ... 
arXiv:0710.1842v1 fatcat:ilosxq4pm5cavdxrwkhn7tnpou

Page 7601 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
of ordered trees with specified degree sequence.  ...  When a, = N, ao = (kK —1)N +1, and all other a;’s are 0, all N-node k-ary trees are generated.” © 2000 Academic Press Stanley Gill Williamson (1-UCSD-CS; La Jolla, CA) 2000k:05012 O05A05 OSAI5S 05A16 S5U10  ... 

Page 1706 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
For each vertex v let d} <--- < dj be the sorted sequence of distances from v to the k vertices in S. For i=1,---,k, let S(v,i) denote the vertex set  ...  Summary: “Let T = (VE) be an undirected tree with positive edge lengths. Let S be a subset of V with |S| =k.  ... 
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