• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.115-123
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• 2004

A recursive tree is constructed by starting with a root node and repeatedly adjoining new nodes to one node of the tree already constructed. Such a tree can represent, for example, the heirarchy of a workforce of a company that grows via recruiting. At times of economic depression, the company may decide to layoff participants, and in some cases it is a fair policy to relieve the last senior worker (most recent entry in the tree). If we remove an edge from such a tree then it falls into two subtrees one of which contains the most recent entry. If we continue to remove edges from the successively smaller subtrees that contain the most recent entry, we eventually isolate the most recent entry. We consider how many randomly selected edges must be removed in average before isolating the most recent entry by this procedure.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.181-192
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• 2003

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.99-103
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• 2003

In this note we find the exact Probability distribution of d$\_$n, i/ the outdegree of the node i, in a random recursive tree with n nodes. For i = i$\_$n/ increasing as a linear function on n, we show that d$\_$n/,i$\_$n/ is asymptotically normal.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.629-640
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• 2000

this paper present an efficient line-drawing algorithm that reduces the amount of space required, Because of its efficiency , this line-drawing algorithm is faster than the Bresenham algorithm or the recursive bisection method. this efficiency was achieved through a new data structure; namely , the modified segment tree (MST). Using the modified segment tree and the distribution rule suggested in this paper, we dra lines without generating the recursive calls used in [3] and without creating the binary operation used in [4]. we also show that line accuracy improves in proportion to the display resolution . In practice, we can significantly improve the algorithm's performance with respect to time and space, This improvement offer an increase in speed, specially with lines at or near horizontal, diagonal. or vertical ; that is, this algorithm requires the time complexity of (n) and the space complexity O(2k+1), where n is the number of pixels and k is a level of the modified segment tree.

• Journal of the Korea Society of Computer and Information
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• v.26 no.2
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• pp.61-68
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• 2021

Recently, various technologies that use machine learning to classify malicious code have been studied. In order to enhance the effectiveness of machine learning, it is most important to extract properties to identify malicious codes and normal binaries. In this paper, we propose a feature extraction method for use in machine learning using recursive methods. The proposed method selects the final feature using recursive methods for individual features to maximize the performance of machine learning. In detail, we use the method of extracting the best performing features among individual feature at each stage, and then combining the extracted features. We extract features with the proposed method and apply them to machine learning algorithms such as Decision Tree, SVM, Random Forest, and KNN, to validate that machine learning performance improves as the steps continue.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.259-263
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• 2007

Which spheres are shellable?[2]. We present one of them which is the k-tree with n-labeled vertices. We found that the number of ways to shell the k-dimensional trees on n-labeled vertices is $$\frac{n!}{(k+1)!}(nk-k^2-k+1)!k$$.

• East Asian mathematical journal
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• v.21 no.2
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• pp.249-260
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• 2005

Experimentation using computer plays an important part in education and research in graph theory. The purpose of this paper is to develop the CAS techniques for the hands-on approach in graph theory specifically on the topic of constructing the spanning tree. This paper discusses the advantages of CAS as the software system for doing graph theory and introduces the software solutions integrating multimedia user interface developed by the author, which extend the functionality of the existing CAS-based graph theory software package.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.4
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• pp.7-14
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• 2003

A number of embedded wavelet image coding methods have been proposed since the introduction of EZW(Embedded Zerotree Wavelet) algorithm. A common characteristic of these methods is that they use fundamental ideas found in the EZW algorithm. Especially, one of these methods is the SPIHT(Set Partitioning in Hierarchy Trees) algorithm, which became very popular since it was able to achieve equal or better performance than EZW without having to use an arithmetic encoder. In this paper We propose a recursive set partitioning in hierarchy trees(RSPIHT) algorithm for embedded image coding and evaluate it's effectiveness experimentally. The proposed RSPIHT algorithm takes the simple and regular form and the worst case time complexity of O(n). From the viewpoint of processing time, the RSPIHT algorithm takes about 16.4% improvement in average than the SPIHT algorithm at T-layer over 4 of experimental images. Also from the viewpoint of coding rate, the RSPIHT algorithm takes similar results at T-layer under 7 but the improved results at other T-layer of experimental images.

• Journal of Broadcast Engineering
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• v.19 no.3
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• pp.405-414
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• 2014

High Efficiency Video Coding(HEVC) obtains high compression ratio by applying recursive quad-tree structured coding unit(CU). However, this recursive quad-tree structure brings very high computational complexity to HEVC encoder. In this paper, we present fast CU decision algorithm in recursive quad-tree structure. The proposed algorithm estimates initial CU size before CTU encoding and checks the proposed condition using Coded Block Flag(CBF) and Rate-distortion cost to achieve the fast encoding time saving. And, intra mode estimation is also possible to be skipped using the CBF values acquired during the inter PU mode estimations. Experiment results shows that the proposed algorithm saved about 49.91% and 37.97% of encoding time according to the weighting condition.

• ETRI Journal
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• v.43 no.6
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• pp.1024-1037
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• 2021

Mining high utility itemsets (HUIs) from transaction databases considers such factors as the unit profit and quantity of purchased items. Two-phase tree-based algorithms transform a database into compressed tree structures and generate candidate patterns through a recursive pattern-growth procedure. This procedure requires a lot of memory and time to construct conditional pattern trees. To address this issue, this study employs two compressed tree structures, namely, Utility Count Tree and String Utility Tree, to enumerate valid patterns and thus promote fast utility computation. Furthermore, the study presents an algorithm called single-phase utility computation (SPUC) that leverages these two tree structures to mine HUIs in a single phase by incorporating novel pruning strategies. Experiments conducted on both real and synthetic datasets demonstrate the superior performance of SPUC compared with IHUP, UP-Growth, and UP-Growth+algorithms.