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A coding algorithm for Rényi trees

William Y.C Chen
1993 Journal of combinatorial theory. Series A  
As a consequence of this decomposition, it immediately follows a coding algorithm for R~nyi trees. We also discuss some applications of our bijections. 1 1 ]=o J =[k(n-k)+l]" k J.  ...  A k-dimensional R~nyi tree is then defined as a k-tree rooted at a given block. C. R~nyi and A.  ...  The author is deeply indebted to him for his inspiring guidance and generous help.  ... 
doi:10.1016/0097-3165(93)90021-y fatcat:2lnb4osq5vfc3aqxnbfaod6z3i

Bijective Linear Time Coding and Decoding for k-Trees

Saverio Caminiti, Emanuele G. Fusco, Rossella Petreschi
2008 Theory of Computing Systems  
In 1970 Rényi and Rényi generalized the Prüfer code, the first bijective code for trees, to a subset of labeled k-trees.  ...  In this paper we introduce a new bijective code for labeled k-trees which, to the best of our knowledge, produces the first coding and decoding algorithms running in linear time with respect to the size  ...  The overall complexity of the decoding algorithm is O(nk). In fact the only step of the algorithm that requires some explanation is Line 7 of Program 8.  ... 
doi:10.1007/s00224-008-9131-0 fatcat:gjycn7xiozd6jmywcpzez4dl4a

Renyi to Renyi -- Source Coding under Siege [article]

Michael B. Baer
2006 arXiv   pre-print
A novel dynamic programming algorithm -- based upon the oldest known algorithm for the traditional alphabetic problem -- optimizes this problem in O(n^3) time and O(n^2) space, whereas two novel approximation  ...  Rather than finding a code minimizing expected codeword length ∑_i=1^n p(i) l(i), the siege problem involves maximizing ∑_i=1^n p(i) θ^l(i) for a known θ∈ (0,1).  ...  David Morgenthaler for discussions and encouragement on this topic, as well as the two anonymous reviewers for suggestions on presentation.  ... 
arXiv:cs/0602067v2 fatcat:a4z7df7nbvdavnfofevmlkic64

Rényi to Rényi ¿ Source Coding under Siege

Michael Baer
2006 2006 IEEE International Symposium on Information Theory  
Rather than finding a code minimizing expected codeword length P n i=1 p(i)l(i), this variant involves maximizing P n i=1 p(i)θ l(i) for a known θ ∈ (0, 1).  ...  A novel dynamic programming algorithm -based upon the oldest known algorithm for the traditional alphabetic problem -optimizes this problem in O(n 3 ) time and O(n 2 ) space, whereas two novel approximation  ...  David Morgenthaler for discussions and encouragement on this topic, as well as the two anonymous reviewers for suggestions on presentation.  ... 
doi:10.1109/isit.2006.262027 dblp:conf/isit/Baer06 fatcat:n4hhkifxr5fujfi5nlzyeziknu

Sequential Multi-Class Labeling in Crowdsourcing [article]

Qiyu Kang, Wee Peng Tay
2018 arXiv   pre-print
As this POMDP formulation is in general intractable, we develop a suboptimal approach based on a q-ary Ulam-Rényi game.  ...  We also propose a sampling heuristic, which can be used in tandem with standard POMDP solvers, using our Ulam-Rényi strategy.  ...  To sample each action inQ, use Algorithm 2 to find a (M, q * , e * ) Ulam-Rényi tree.  ... 
arXiv:1711.02128v2 fatcat:hedf2ucetrbjth37ajnppuwgta

Comparison of Decision Trees with Rényi and Tsallis Entropy Applied for Imbalanced Churn Dataset

Krzysztof Gajowniczek, Tomasz Ząbkowski, Arkadiusz Orłowski
2015 Proceedings of the 2015 Federated Conference on Computer Science and Information Systems  
Two algorithms for building classification trees, based on Tsallis and Rényi entropy, are proposed and applied to customer churn problem.  ...  The quality measures for obtained trees are compared for different values of α parameter.  ...  ACKNOWLEDGMENT The computations were performed partially employing the computational resources of the Interdisciplinary Centre for Mathematical and Computational Modeling at the Warsaw University (Computational  ... 
doi:10.15439/2015f121 dblp:conf/fedcsis/GajowniczekZO15 fatcat:6idp5fb2jbbthb44nxdpkmor5e

A compact code for k-trees

Lilian Markenzon, Oswaldo Vernet, Paulo Renato da Costa Pereira
2009 Pesquisa Operacional  
In this paper, we propose a new representation for k-trees - the compact code, which reduces the required memory space from O(nk) to O(n).  ...  The encoding and decoding algorithms, based on a simplification of a priority queue, are linear and very simple.  ...  In Rényi and Rényi (1970) , the redundant Prüfer code for k-trees was defined and used by the authors in the counting of labelled k-trees.  ... 
doi:10.1590/s0101-74382009000300001 fatcat:mv7cjz32vvhqnldua7mbaulk7u

Page 882 of Mathematical Reviews Vol. 46, Issue 4 [page]

1973 Mathematical Reviews  
Sedidéek (Prague) Rényi, C. [Rényi, Katé]; Rényi, A. 5153 The Priifer code for k-trees Combinatorial Theory and its Applications, III (Proc. Collog., Balatonfiired, 1969), pp. 945-971.  ...  K. 5154 An algorithm for the solution of certain extremal prob- lems on a tree. (Russian) Prikl. Mat. i Programmirovanie Vyp. 7 (1972), 43-47. ‘Let H=(X, V) be a tree with n vertices.  ... 

Modulation Signal Recognition Based on Information Entropy and Ensemble Learning

Zhen Zhang, Yibing Li, Shanshan Jin, Zhaoyue Zhang, Hui Wang, Lin Qi, Ruolin Zhou
2018 Entropy  
a 34% increase when using SVM classifier.  ...  The simulation results show that the feature subsets selected by SFS and SFFS algorithms are the best, with a 48% increase in recognition rate over the original feature set when using KNN classifier and  ...  The same code runs on major distributed environment that can solve problems for more than billions of examples.  ... 
doi:10.3390/e20030198 pmid:33265289 fatcat:cp7vsji2ebefbnlbfj5u5amduu

An Empirical Investigation of Attribute Selection Techniques based on Shannon, Rényi and Tsallis Entropies for Network Intrusion Detection

Christiane Ferreira Lemos Lima, Francisco M. de Assis, Cleonilson Protásio de Souza
2012 American Journal of Intelligent Systems  
In this context, selecting optimal attributes is a difficult task considering that the set of all attributes can assume a huge variety of data formats (for examp le: symbol set, e.g. binary, alphanumeric  ...  Intrusion Detection Systems of computer network perform their detection capabilit ies by monitoring a set of attributes from network traffic.  ...  ACKNOWLEDGEMENTS The authors would like to thank Brazilian Coordination for Improvement of Higher Education Personal (CAPES), National Council fo r Scientific and Technological Develop ment (CNPq) and  ... 
doi:10.5923/j.ajis.20120205.05 fatcat:f2pmul73mfdkridr2onn32bq7u

The Renyi redundancy of generalized Huffman codes

A.C. Blumer, R.J. McEliece
1988 IEEE Transactions on Information Theory  
If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes.  ...  In 1965, Campbell [1] showed that just as the Shannon entropy is a lower bound on the average codeword length of a uniquely decodable code, the Renyi entropy is a lower bound on the exponentially weighted  ...  An item is found when a leaf is reached. The items correspond to the source symbols in Huffman coding, and Huffman's algorithm constructs the tree which minimizes the average search time.  ... 
doi:10.1109/18.21251 fatcat:dc52iecranguvm5c23yjqr3kbi


The Renyi entropy is a one-parameter generalization of the Shannon entropy. Here Renyi entropy was calculated for the one-dimensional histogram of the images.  ...  In this paper, edge detection in gray level images is done by using Renyi entropy and particle swarm optimization (PSO) algorithm.  ...  This approach may be used in any decision tree and information selection algorithm.  ... 
doi:10.34218/ijaret.11.6.2020.112 fatcat:uktyetunanbldmqnq5qyigrzvu

Graph Compression with Application to Model Selection [article]

Mojtaba Abolfazli, Anders Host-Madsen, June Zhang, Andras Bratincsak
2021 arXiv   pre-print
We encode in two steps: 1) transforming graph into a rooted binary tree, 2) the encoding rooted binary tree using graph statistics.  ...  In this paper, we present universal source coding methods for the lossless compression of unweighted, undirected, unlabelled graphs.  ...  the tree T (e.g., p or p when using triangles for coding).  ... 
arXiv:2110.00701v1 fatcat:2sdp2f3o6ngndd2xdolw3ma72i


2010 Discrete Applied Mathematics  
Parker Interlace polynomials: Enumeration, unimodality and connections to codes 636 H. Hajiabolhassan and A. Cheraghi Bounds for visual cryptography schemes 659 J. Huang and B. Xu  ...  Ghosh Approximation algorithms for art gallery problems in polygons 718 Z. Király, B. Cosh and B.  ... 
doi:10.1016/s0166-218x(10)00054-5 fatcat:oxwaaoup3besdcn5z7htv7cwsa

Local Structure Theorems for Erdos Renyi Graphs and their Algorithmic Application [article]

Jan Dreier, Philipp Kuinke, Ba Le Xuan, Peter Rossmanith
2018 arXiv   pre-print
The local structure of sparse Erdos-Renyi Gaphs is very special: The r-neighborhood of a vertex is a tree with some additional edges, where the probability that there are m additional edges decreases with  ...  This implies efficient algorithms for subgraph isomorphism, in particular for finding subgraphs with small diameter.  ...  In Section 4 we use the locally tree-like structure of Erdős-Rényi graphs to construct an efficient algorithm for subgraph isomorphism.  ... 
arXiv:1709.09152v2 fatcat:zgpfy23yvbdcngrsavnaomgjqa
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