An Evaluation of the Critical Factors Affecting the Efficiency of Some Sorting Techniques

In computer science study, much importance is attached to the way in which data are arranged. Data can be arranged in clustered form or grain (scattered or loosely) form. Information about data arrangement is very important because it is a predominant factor in accessing the data. Any data that is not easily accessible to the user is not good and may be difficult to use. In other to make data useful and accessible at any given time the arrangement of the data in memory should be orderly. This orderly arrangement of data is referred to as sorting. Sorting can also mean the process of arranging items in sequence form and/or in different sets, and accordingly. Data can be sorted according to their kind, class, nature and so on. This ordering makes it possible or easy to search for a specific data or elements in the sorted list. Another important aspect in computer science is efficiency; therefore data are sorted in other to gain efficiency in retrieving or searching task.

Statistical analysis has been a useful tool in nearly all the fields of study, for example, Engineering, Science, Journalism, and Marketing. The field of statistics has been very useful when tasks involve estimating or analyzing values. The most recognized statistical package in use by many researchers is the Statistical Packages for Social Sciences (SPSS). There are several methods of data analysis in SPSS which include general linear model, generalized linear models, mixed models, compare means, dimension reduction, log-linear, nonparametric test, scales, survivals, forecasting, missing value analysis, multiple imputation, complex samples, quality control and so on.

In this work, factor analysis which is a branch of dimension reduction method is used. It seeks to discover if the observed variables can be interpreted in a more compressed form with few numbers of variables called factors. Sorting is an important process that determines the efficiency of many computing tasks and procedures. The speed of a particular sorting technique used in a task will determine how fast such task can be completed. Hence the efficiency of sorting technique affects to a large extent the efficiency of computing procedures [1].

This study evaluated the critical factors that affect the efficiency of sorting techniques. The objectives of the study are:

• (i)    To carry out an exploratory study of critical factors affecting the efficiency of Shell, Bubble, Heap, Quick and Merge sorts.

• (ii)    To conduct experiments in order to determine the efficiency of these sorting techniques mentioned in (i) above in terms of execution time, memory used and the number of exchanges/comparisons.

• (iii)    To subject the result obtained in (ii) above to factor analysis by SPSS.

Factor analysis was first introduced by Thurstone in 1931. The main general purposes of introducing the techniques are to reduce the number of variables and to detect structure in the relationships between variables, i.e. to classify variables. Therefore, factor analysis is applied as data reduction or structure detection method. Factor analysis originated in psychometrics, and is used in behavioural sciences, social sciences, marketing, product management, operations research, and other applied sciences that deal with large quantities of data.

Factor analysis attempts to identify underlying variables or factors that explain the pattern of correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance observed in a much larger number or manifest variables. It is assumed that data should have a bivariate normal distribution for each pair of variables and observations should be independent. Using Factor analysis method under SPSS for specifying and capturing of the variables involves the following four procedural steps: Descriptive, Extraction, Rotation, Factor Scores, and Options methods [2]. Each of these categories also contains other alternatives to be selected depending on the type of analysis.

There are basically two types of factor analysis: Exploratory factor analysis (EFA) and Confirmatory factor analysis (CFA). Both types of factor analyses are based on the Common Factor Model. Exploratory Factor Analysis (EFA) attempts to discover the nature of the constructs influencing a set of responses. It is used to uncover the underlying structure of a relatively large set of variables. It is the common form of factor analysis. Confirmatory Factor Analysis (CFA) tests whether a specified set of constructs is influencing responses in a predicted way. It determines if the number of factors and the loadings of measured variables on them conform to what is expected on the basis of pre-established theory.

There are different types of factoring, these include principal factor also referred to as Principal Component Analysis (PCA). It seeks a linear combination of variables such that the maximum variance is extracted from the variables. It then removes this variance and seeks a second linear combination which explains the maximum proportion of the remaining variance, and so on. This is called the principal axis method and results in orthogonal (uncorrelated) factors. Another type of factoring is referred to as Canonical Factor Analysis (CFA): It is also called Rao’s canonical factoring. CFA seeks factors which have the highest canonical correlation with the observed variables. CFA is unaffected by arbitrary rescaling in the data.

Other types of factoring include Principal Factor Analysis (PFA) or Principal Axis Factoring (PAF), Image Factoring, Alpha Factoring etc. The remaining part of this paper is organized as follows: Section II presents some literature review on sorting techniques and factor analysis, Section III describes the methodology, Section IV presents the result and Section V concludes the paper.

• II.    RELATED WORK