Complexity Analysis Involving Heterogeneous System

Abstract

Complexity analysis is one of the most complicated topics in mathematics. It involves an unusual concept and some tricky algebra. This report is a humble trail to demystify the idea in detail. Heterogonous systems are becoming bigger and more complex. While the complexity of large-scale heterogeneous systems has been acknowledged to be an important challenge, there has not been much work in defining or measuring system complexity. Thus, today, it is difficult to compare the complexities of different systems, or to state that one system is easier to program, to manage or to use than another. Here we try to understand the factors that cause heterogeneous systems to appear very complex to people. We define different aspects of system complexity and propose metrics for measuring these aspects. We also show how these aspects affect the system. Based on the aspects and metrics of complexity, we propose general guidelines that can help to measure the complexity of systems. There are many types of analysis and various methods available to analyze the algorithms like apriori analysis, posterior analysis, micro analysis, macro analysis, amortized analysis, big O notation, theta notation, potential method, accounting method. All analysis and methods are situation specific. Our report does a comparative study of various method and techniques of algorithm analysis giving their specific advantages and disadvantages. In this report online banking system is discussed in detail. In this systems there are various factors that will play significant roles in the overall complexity, there are many algorithms that are running simultaneously like fault tolerance, authentication, encryption, routing tables, communication protocols and for error recovery. Every algorithm contributes in the system. In this report we will measure how much contribution they have. Every algorithm have time and space complexity, if the algorithms are running parallel then the complexity will be highest out of them . E.g. we have complexities n, n+1,n2 then the complexity will be n2. If we have N algorithms and they are running sequentially then the complexity will be sum of all these.eg. We have N algorithms running simultaneously then the total complexity will be Tc = 1+2+……+N.