scholarly journals Time Complexity Analysis of the Binary Tree Roll Algorithm

2017 ◽  
Vol 12 (2) ◽  
Author(s):  
Adrijan Božinovski ◽  
George Tanev ◽  
Biljana Stojčevska ◽  
Veno Pačovski ◽  
Nevena Ackovska
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Binary Tree ◽  
Time Complexity ◽  
Recurrence Relations ◽  
Complexity Analysis ◽  
Worst Case ◽  
Average Case ◽  
The Empirical Analysis

This paper presents the time complexity analysis of the Binary Tree Roll algorithm. The time complexity is analyzed theoretically and the results are then confirmed empirically. The theoretical analysis consists of finding recurrence relations for the time complexity, and solving them using various methods. The empirical analysis consists of exhaustively testing all trees with given numbers of nodes  and counting the minimum and maximum steps necessary to complete the roll algorithm. The time complexity is shown, both theoretically and empirically, to be linear in the best case and quadratic in the worst case, whereas its average case is shown to be dominantly linear for trees with a relatively small number of nodes and dominantly quadratic otherwise.

scholarly journals Space Complexity Analysis of the Binary Tree Roll Algorithm

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Adrijan Božinovski ◽  
George Tanev ◽  
Biljana Stojčevska ◽  
Veno Pačovski ◽  
Nevena Ackovska
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Binary Tree ◽  
Complexity Analysis ◽  
Space Complexity ◽  
Worst Case ◽  
Average Case ◽  
Tree Topologies ◽  
The Given ◽  
The Empirical Analysis

This paper presents the space complexity analysis of the Binary Tree Roll algorithm. The space complexity is analyzed theoretically and the results are then confirmed empirically. The theoretical analysis consists of determining the amount of memory occupied during the execution of the algorithm and deriving functions of it, in terms of the number of nodes of the tree n, for the worst - and best-case scenarios. The empirical analysis of the space complexity consists of measuring the maximum and minimum amounts of memory occupied during the execution of the algorithm, for all binary tree topologies with the given number of nodes. The space complexity is shown, both theoretically and empirically, to be logarithmic in the best case and linear in the worst case, whereas its average case is shown to be dominantly logarithmic.

scholarly journals CONFLICTOLOGICAL CULTURE OF PERSONALITY IN A PROFESSIONAL ENVIRONMENT (BY THE EXAMPLE OF PEDAGOGUES AND ENGINEERS)

2016 ◽  
Vol 1 ◽  
pp. 524 ◽  
Author(s):  
Olga Shcherbakova ◽  
Anna Tatarinceva
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Work Experience ◽  
Scientific Literature ◽  
Gender And Work ◽  
Professional Environment ◽  
The Given ◽  
The Empirical Analysis

The levels of conflictological culture of pedagogues and engineers, the peculiarities of its formation as well as the comparison of the conflictological culture’s levels among representatives of these specialties on the base of their gender and work experience are analyzed in the proposed research. Each specialist owns a certain level of the conflictological culture’s development and he/she expresses it in a professional environment. The relevance of the research’s theme is caused by the necessity to improve conflictological culture of specialists for their further successful activities. The Aim of the research is the identification of differences in the levels’ formation of specialists’ conflictological culture by the example of pedagogues and engineers and the influence of such a characteristic as a gender and work experience  on it. The Object of the research is the process of forming conflictological culture of pedagogues and engineers. The Methods of the research are the following:1. the theoretical analysis of scientific literature on the given problem;2.the empirical analysis of obtained data reflected the level’s formation of pedagogues and engineers. 

scholarly journals TIME OPTIMAL ALGORITHMS FOR BLACK HOLE SEARCH IN RINGS

2011 ◽  
Vol 03 (04) ◽  
pp. 457-471 ◽  
Author(s):  
B. BALAMOHAN ◽  
P. FLOCCHINI ◽  
A. MIRI ◽  
N. SANTORO
Keyword(s):  
Black Hole ◽  
Time Complexity ◽  
Time Cost ◽  
Ring Networks ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Time Optimal ◽  
Optimal Average

In a network environment supporting mobile entities (called robots or agents), a black hole is a harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problit is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper, we consider the black hole search problit in asynchronous ring networks of n nodes, and focus on time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n - 2) time in the worst case. The best known algorithm achieves this bound with a team of n - 1 agents with an average time cost of 2(n - 2), equal to the worst case. In this paper, we first show how the same number of agents using 2 extra time units in the worst case, can solve the problit in only [Formula: see text] time on the average. We then prove that the optimal average case complexity of [Formula: see text] can be achieved without increasing the worst case using 2(n - 1) agents. Finally, we design an algorithm that achieves asymptotically optimal both worst and average case time complexities itploying an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.

scholarly journals d-PBWT: dynamic positional Burrows-Wheeler transform

2020 ◽  
Author(s):  
Ahsan Sanaullah ◽  
Degui Zhi ◽  
Shaojie Zhang
Keyword(s):  
Data Structure ◽  
Time Complexity ◽  
Linear Time ◽  
Genotype Imputation ◽  
Worst Case ◽  
Average Case ◽  
Insertion And Deletion ◽  
Static Data ◽  
Efficient Retrieval ◽  
Burrows Wheeler Transform

AbstractDurbin’s PBWT, a scalable data structure for haplotype matching, has been successfully applied to identical by descent (IBD) segment identification and genotype imputation. Once the PBWT of a haplotype panel is constructed, it supports efficient retrieval of all shared long segments among all individuals (long matches) and efficient query between an external haplotype and the panel. However, the standard PBWT is an array-based static data structure and does not support dynamic updates of the panel. Here, we generalize the static PBWT to a dynamic data structure, d-PBWT, where the reverse prefix sorting at each position is represented by linked lists. We developed efficient algorithms for insertion and deletion of individual haplotypes. In addition, we verified that d-PBWT can support all algorithms of PBWT. In doing so, we systematically investigated variations of set maximal match and long match query algorithms: while they all have average case time complexity independent of database size, they have different worst case complexities, linear time complexity with the size of the genome, and dependency on additional data structures.

scholarly journals Risk Measurement by G-Expected Shortfall

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Ziting Pei ◽  
Xuhui Wang ◽  
Xingye Yue
Keyword(s):  
Explicit Formula ◽  
Empirical Analysis ◽  
Risk Measure ◽  
Computational Cost ◽  
Expected Shortfall ◽  
Risk Measurement ◽  
Worst Case ◽  
New Type ◽  
The Empirical Analysis ◽  
Low Computational Cost

G-expected shortfall (G-ES), which is a new type of worst-case expected shortfall (ES), is defined as measuring risk under infinite distributions induced by volatility uncertainty. Compared with extant notions of the worst-case ES, the G-ES can be computed using an explicit formula with low computational cost. We also conduct backtests for the G-ES. The empirical analysis demonstrates that the G-ES is a reliable risk measure.

Complexity Analysis of Neural Network Based on Rational Spline Weight Functions

2014 ◽  
Vol 644-650 ◽  
pp. 1658-1661
Author(s):  
Dai Yuan Zhang ◽  
Hai Nan Yang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Theoretical Analysis ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Weight Functions ◽  
Rational Spline ◽  
The Neural Network ◽  
The Neural Networks

This paper aims to obtain the time complexity for a new kind of neural network using rational spline weight functions. In this paper, we introduce the architecture of the neural network, and analyze the time complexity in detail. Finally, some examples are also given to verify the theoretical analysis. The results show that the time complexity depends on the number of patterns, the input and out dimensions of the neural networks.

Complexity Research on B Algorithm

2010 ◽  
Vol 20-23 ◽  
pp. 173-177
Author(s):  
Ai Li Han
Keyword(s):  
Time Complexity ◽  
Complexity Analysis ◽  
Search Algorithms ◽  
Heuristic Function ◽  
Worst Case ◽  
Intelligent Search ◽  
The Cost

The time complexity of B algorithm, one of the intelligent search algorithms, is discussed. By anatomizing some instances, it is pointed out that the cost of calculating the value of heuristic function should be included in the range of time complexity analysis for B algorithm. And then, an algorithm of calculating the value of heuristic function is presented. By analyzing the cost of calculating the value of heuristic function, it is pointed out that the number of recursions in B algorithm is O(n!) in the worst case. Therefore, the time complexity of B algorithm is exponential instead of O(n2).

scholarly journals Audiovisual cultural artifacts of protest in the Basque Country

2014 ◽  
Vol 20 (2) ◽  
pp. 224 ◽  
Author(s):  
Arkaitz Letamendia
Keyword(s):  
Theoretical Analysis ◽  
Empirical Analysis ◽  
Basque Country ◽  
Theoretical Discussion ◽  
Visual Sociology ◽  
Alternative Communication ◽  
Cultural Artifacts ◽  
Cultural Artifact ◽  
Complex Relationships ◽  
The Empirical Analysis

In this article we propose the emergence of a new kind of visual protest and alternative communication called the Audiovisual Cultural Artifact of Protest (ACAP). These will be studied in the context of the Basque Country, which currently combines structural and conjunctural characteristics that make it an outstanding laboratory for the study of these artifacts. A theoretical analysis of the complex relationships between power, communication and resistance will be carried out, and a reading is proposed that deals with the different planes on which these resistances and disputes are expressed. Based on this analysis, four kinds of audiovisual artifacts produced in the Basque Country are studied. For the empirical analysis, the methodological reflections of visual sociology are taken into consideration. The results provide an overview of these Audiovisual Cultural Artifacts of Protest and the theoretical discussion confirms the emergence of these new forms of visual protest, indicating the existence of a broad-based dynamic in which their proliferation and diversification is occurring. The analysis of the case of the Basque Country allows these tactical and communicative innovations to be contextualised and a discussion to take place about the importance of that context, the discourse’s construction and the possible trend towards spectacularisation of the resistances.Caption: #U12Bilbora: MobiLIPDUBzioa Durangon (2012).

FORMATION AND URGENCY OF THE CONCEPT `MUSICAL TASTE`: FROM ANCIENT TIMES TILL NOWADAYS

2015 ◽  
pp. 46
Author(s):  
Marina Marčenoka
Keyword(s):  
Theoretical Analysis ◽  
Music Education ◽  
Retrospective Analysis ◽  
Empirical Analysis ◽  
Contemporary Society ◽  
Musical Preference ◽  
Musical Taste ◽  
Ancient Times ◽  
The Empirical Analysis ◽  
Education Process

<p>The aim of the paper is a retrospective analysis of formation of the 'musical taste' concept and its urgency in the contemporary society. The Methods of the research are: the theoretical analysis of the philosophical and musical literature on the approaches to the concepts “esthetical taste” (C. Batteux, D. Hume, C. Montesquieu, M. Zeltser, F. Hutcheson, A. Shafstbery, J. Herder), “artistic taste” (L. Kogan), “musical taste” (M. Marchenoka); the theoretical analysis of the psychological literature on the approaches to the problem of musical taste in the contemporary society (A. North, J. Charles &amp; L. Sant-Kvinton, P. Rentfrow &amp; S. Gosling); the empirical analysis of musical preference in the music education process (M. Marchenoka). The Results of the research are the following: in the research the essence of the musical taste is defined and is examined its urgency in the contemporary society and the empirical analysis of musical preference in the music education process.</p>

An Efficient Algorithm for Automating Classification of Chemical Reactions into Classes in Ugi’s Reaction Scheme

2012 ◽  
Vol 2 (2) ◽  
pp. 1-14 ◽  
Author(s):  
Sanjay Ram ◽  
Somnath Pal
Keyword(s):  
Chemical Reactions ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Symmetric Matrix ◽  
Reaction Scheme ◽  
Space Complexity ◽  
Worst Case ◽  
Average Case ◽  
Model Driven

There are two approaches for classification of chemical reactions: Model-Driven and Data-Driven. In this paper, the authors develop an efficient algorithm based on a model-driven approach developed by Ugi and co-workers for classification of chemical reactions. The authors’ algorithm takes reaction matrix of a chemical reaction as input and generates its appropriate class as output. Reaction matrices being symmetric, matrix implementation of Ugi’s scheme using upper/lower tri-angular matrix is of O(n2) in terms of space complexity. Time complexity of similar matrix implementation is O(n4), both in worst case as well as in average case. The proposed algorithm uses two fixed size look-up tables in a novel way and requires constant space complexity. Time complexity both in worst and average cases of the algorithm is linear.

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