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On coding labeled trees

Saverio Caminiti, Irene Finocchi, Rossella Petreschi
2007 Theoretical Computer Science  
We consider the problem of coding labeled trees by means of strings of node labels. Different codes have been introduced in the literature by Prüfer, Neville, and Deo and Micikevičius.  ...  These schemes can be parallelized on the EREW PRAM model, so as to work in O(log n) time with cost O(n), O(n log n), or O(n log n), depending on the code and on the operation: in all cases, they either  ...  An interesting alternative to the usual representations of tree data structures in computer memories is based on coding labeled trees by means of strings of node labels.  ... 
doi:10.1016/j.tcs.2007.03.009 fatcat:xhvhhrf37fhzvaqwb4wuhslvte

Branch Code: A Labeling Scheme for Efficient Query Answering on Trees

Yanghua Xiao, Ji Hong, Wanyun Cui, Zhenying He, Wei Wang, Guodong Feng
2012 2012 IEEE 28th International Conference on Data Engineering  
trees, these labeling schemes usually show weakness in one aspect or another.  ...  The proposed branch code can answer common queries on ordered trees in constant time, which comes at the cost of consuming O(N log N ) storage.  ...  To test the efficiency of our labeling schemes on dynamic trees, we simulate From the results, we can see our query answering solution by branch code on dynamic tree performs better than Dewey labeling  ... 
doi:10.1109/icde.2012.71 dblp:conf/icde/XiaoHCHWF12 fatcat:brfgaheilfe2fpk6qc3q7cwule

A Generalized Enumeration of Labeled Trees and Reverse Prüfer Algorithm [article]

Seunghyun Seo, Heesung Shin
2005 arXiv   pre-print
A leader of a tree T on [n] is a vertex which has no smaller descendants in T.  ...  Gessel and Seo showed ∑_T ∈T_nu^(# of leaders in T) c^(degree of 1 in T)=u P_n-1(1,u,cu), which is a generalization of Cayley formula, where T_n is the set of trees on [n] and P_n(a,b,c)=c∏_i=1^n-1(ia+  ...  We can find the tree T whose code is σ as building up labeled trees T i with i + 1 vertices, except one leaf is unlabeled, by reading the code σ forward.  ... 
arXiv:math/0601009v1 fatcat:umnfx2vgyzgnxkfzbztzmtj4zq

Gray coding planar maps [article]

Sergey Avgustinovich, Sergey Kitaev, Vladimir N. Potapov, Vincent Vajnovszki
2015 arXiv   pre-print
In this paper, we utilize beta-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps  ...  The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way.  ...  The second author is grateful to London Mathematical Society and to the University of Bourgogne for supporting his work on this paper.  ... 
arXiv:1509.05807v1 fatcat:sxxooo2zmzdyhnjvkls5cysb5i

Short Labels for Lowest Common Ancestors in Trees [chapter]

Johannes Fischer
2009 Lecture Notes in Computer Science  
We then perform a thorough experimental evaluation of these schemes on a variety of tree shapes and sizes.  ...  We evaluate the practical performance of labeling schemes for lowest common ancestors in trees. We develop different variants for encoding the labels.  ...  Further thanks go to Simon Gog for his broadword-implementation of the Fibonacci-and Ternary Coding.  ... 
doi:10.1007/978-3-642-04128-0_67 fatcat:uk7t347r6vdivgeippbxsbtfby

Gray coding cubic planar maps

Sergey Avgustinovich, Sergey Kitaev, Vladimir N. Potapov, Vincent Vajnovszki
2016 Theoretical Computer Science  
A loop is a closed curve which contains Key words and phrases. planar map, bicubic planar map, cubic non-separable planar map, 3-connected cubic planar map, Gray code, description tree, β(0, 1)-tree.  ...  On the other hand, the area of combinatorial Gray codes was popularized by Herbert Wilf in 1988-89 and since then such codes were found for many combinatorial structures, e.g. for involutions and fixed-point  ...  The second author is grateful to London Mathematical Society and to the University of Bourgogne for supporting his work on this paper.  ... 
doi:10.1016/j.tcs.2015.12.013 fatcat:nku7atrpirf3xcnnevbp3bir5m

An Optimal Algorithm for Prufer Codes

Xiaodong Wang, Lei Wang, Yingjie Wu
2009 Journal of Software Engineering and Applications  
This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree.  ...  The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually.  ...  An interesting alternative to the usual representations of tree data structures in computer memories is based on coding labeled trees by means of strings of node labels.  ... 
doi:10.4236/jsea.2009.22016 fatcat:z4wnmlswgjgzfmd7diwuz5c5py

A generalized enumeration of labeled trees and reverse Prüfer algorithm

Seunghyun Seo, Heesung Shin
2007 Journal of combinatorial theory. Series A  
Gessel and Seo showed that which is a generalization of Cayley's formula, where T n is the set of trees on [n] and P n (a, b, c Using a variation of the Prüfer code which is called a RP-code, we give a  ...  A leader of a tree T on [n] is a vertex which has no smaller descendants in T .  ...  We can find the rooted tree T whose code is σ by building trees T i with i labeled vertices and one unlabeled leaf by reading the code σ from left to right.  ... 
doi:10.1016/j.jcta.2007.01.010 fatcat:pzi7xcxfvfa33jiufrrerc62b4

Bijective Linear Time Coding and Decoding for k-Trees

Saverio Caminiti, Emanuele G. Fusco, Rossella Petreschi
2008 Theory of Computing Systems  
The problem of coding labeled trees has been widely studied in the literature and several bijective codes that realize associations between labeled trees and sequences of labels have been presented. k-trees  ...  In 1970 Rényi and Rényi generalized the Prüfer code, the first bijective code for trees, to a subset of labeled k-trees.  ...  Here we show a generalization of one of these codes, that takes into account labels on edges and can be use to code characteristic trees of Rényi k-trees.  ... 
doi:10.1007/s00224-008-9131-0 fatcat:gjycn7xiozd6jmywcpzez4dl4a

A Unified Approach to Coding Labeled Trees [chapter]

Saverio Caminiti, Irene Finocchi, Rossella Petreschi
2004 Lecture Notes in Computer Science  
We consider the problem of coding labeled trees by means of strings of node labels and we present a unified approach based on a reduction of both coding and decoding to integer (radix) sorting.  ...  The algorithm can be parallelized on the EREW PRAM model, so as to work in O(log n) time using O(n) or O(n √ log n) operations, depending on the code.  ...  The coding scheme is based on the definition of pairs associated to the nodes of the tree according to some criteria dependent on the specific code.  ... 
doi:10.1007/978-3-540-24698-5_38 fatcat:naxspbtrqfacnlvzqk57ggl764

Algorithms for Indexing Dynamic XML Data

Jeang-Kuo Chen, Jen-Peng Hsu
2006 Proceedings of the 9th Joint Conference on Information Sciences (JCIS)  
When updating the index tree, we use a new label coding method for new-inserted nodes.  ...  If LSDX inserts a new node C between two nodes A, B and then inserts a new node D between the two nodes A, C, the label of the node D cannot be coded because of the label coding strategy of LSDX.  ...  Fig. 2 : The node structure of an XML index tree. 2.2. The coding rule of node label for building an index tree When LSDX builds an index tree, the coding rule of node label is as follows.  ... 
doi:10.2991/jcis.2006.333 dblp:conf/jcis/ChenH06 fatcat:c4sd6yvvbzab5ir3rtijqdze2y

Short Labels by Traversal and Jumping

Nicolas Bonichon, Cyril Gavoille, Arnaud Labourel
2007 Electronic Notes in Discrete Mathematics  
Our scheme, called Traversal & Jumping, assigns to the n vertices of any bounded degree tree distinct binary labels of log 2 n + O(1) bits in O(n) time such that we can compute adjacency between two vertices  ...  only from their labels.  ...  Three conditions on p i (and so on t i ) have to be satisfied to ensure that the code is valid.  ... 
doi:10.1016/j.endm.2007.01.022 fatcat:pdo4ksdd4faqzgz7tjks7xhmwa

Efficient Label Encoding for Range-Based Dynamic XML Labeling Schemes [chapter]

Liang Xu, Tok Wang Ling, Zhifeng Bao, Huayu Wu
2010 Lecture Notes in Computer Science  
We introduce a novel Search Tree-based (ST) encoding technique to overcome these problems.  ...  We show that ST encoding is widely applicable to different dynamic labels and prove the optimality of our results.  ...  The resulting label size is also optimal because our algorithm favors STQ codes with smaller lengths. ST-Vector (STV) Our STV encoding scheme is based on the data structure we call STV tree.  ... 
doi:10.1007/978-3-642-12026-8_21 fatcat:ay6zxc2p3ndt5f2su25xiryhqq

A New Coding Technique and Analysis of Trees

2020 International journal of recent technology and engineering  
Then we get the encoded message as Ciphertext with a binary tree. Using the binary tree we form a prefix code of Huffman coding and we define a new labeling function of edge and vertex labeling.  ...  A message is encoded using one-time pad Cipher and Huffman coding with certain algorithm. Encoding process is done using a symmetric key known to sender and receiver.  ...  Inspired by these work on trees we found a new methods of coding by Huffman algorithm.  ... 
doi:10.35940/ijrte.d1027.1284s519 fatcat:4zw7t7z6ovdu5bpdtvffuyn5fq

String Coding of Trees with Locality and Heritability [chapter]

Saverio Caminiti, Rossella Petreschi
2005 Lecture Notes in Computer Science  
We consider the problem of coding labelled trees by means of strings of vertex labels and we present a general scheme to define bijective codes based on the transformation of a tree into a functional digraph  ...  Looking at the fields in which codes for labelled trees are utilized, we see that the properties of locality and heritability are required and that codes like the well known Prüfer code do not satisfy  ...  Dandelion code In the following we present the Dandelion code as introduced in [10] with labels on edges: Dandelion Coding Algorithm Input: Input: an n-tree T Output: Output: an (n − 2)-string C 1.  ... 
doi:10.1007/11533719_27 fatcat:2p2b4orcyrdpref55ymiels4ke
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