Algorithm Analysis: Understanding Efficiency and Complexity Concepts

This homework assignment delves into the core concepts of algorithm analysis, a critical component of computer science. The paper begins with a definition of algorithm analysis, emphasizing its role in providing theoretical estimations for algorithms and its application in solving computational problems. It explores time and space complexity, explaining how these measurements are used to assess the resources required by an algorithm. The assignment discusses the significance of algorithm efficiency, highlighting the importance of minimizing both time and space complexity. Various notations, such as Big O, Big Theta, and Big Omega are mentioned as tools for measuring complexity. The paper also touches upon the steps involved in a complete algorithm analysis process, including implementation, time measurement, and the production of a realistic system for input signals. Furthermore, the assignment explores algorithm efficiency, defining it in relation to computational resources and the concept of time and space efficiency. Finally, the paper discusses the efficiency of bubble sort processes and the application of small-o complexity.

Running Head: ALGORITHM ANALYSIS
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Algorithm analysis

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Algorithm Analysis
The term algorithm analysis was given by Donald Knuth and it is a very important
part of computer theory that produces theoretical estimation for an algorithm. It is a
type of process which is also used to solve a particular computational problem. Many of
algorithm processes are developed to work with input of arbitrary length and algorithm
analysis is a measurement method which is used to calculate time and space required to
solve an algorithm (Saunders, Russell, & Crabb, 2015). It is observed that the running
time of any source code is started as a function which is related to the input length and
this process is called as time complexity. The algorithm is a different process and
objective of an algorithm process is to understand the concept of any programming. In
the field of computer science, it is a process to determine the computational complexity
of an algorithm (Saunders, Russell, & Crabb, 2015). It is researched that an algorithm is
called as more efficient when values of time complexity and space complexity are very
small as compare to the size of input signals. In this type of process big O notation, big
theta notation and big omega notation are used to measure time and space complexity
of any source code (Saunders, Russell, & Crabb, 2015).
The main aim of algorithm analysis is to determine the overall performance of
various algorithms in order to design decisions (Tsoukalas, & Fragiadakis, 2016). A
complete algorithm analysis process involves a few steps which are following
 Implement an algorithm process
 Measure the time required to perform each operation
 Investigate unknown quantities
 Produce a realistic system for the input signals

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 Determine time complexity and space complexity for particular source code
(Tsoukalas, & Fragiadakis, 2016).
Algorithm Efficiency
In the field of computer science, the efficiency of an algorithm is a property of
any source code that is related to various computational resources. Algorithm efficiency
is defined as analogous to improve the productivity of any computer devices and for
maximum efficiency; people can reduce the use of additional resources (Ahmed, &
Salam, 2015). It is estimated that different resources, for example, time and space
cannot be compared directly, therefore, two algorithm process is used to measure the
efficiency of any source code (Ahmed, & Salam, 2015). Algorithm efficiency was
developed by Ada Lovelace in the year 1843 and it is divided into two parts such as time
and space efficiency.
Time efficiency is used to determine the total amount of time taken by the
algorithm to execute particular task and space efficiency is used to calculate to space
required to execute an algorithm process (Yu, Li, Jia, Zhang, & Wang, 2015). For bubble
sort processes the overall efficiency is given by O(N2) and in which N/2 comparison is
needed to perform one task at a time. It is researched that when the order of two or
more algorithm processes are the same than their efficiency are also equal in terms of
computation. The main advantage of this process is to implement the difficulties and
problems of any source code (Yu, Li, Jia, Zhang, & Wang, 2015). Small-o complexity is a
process which is used in algorithm efficiency and it calculates the total time needed to
execute the algorithm. Therefore users can understand time and space complexity by

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algorithm efficiency and they can easily calculate both quantities for any source code
(Yu, Li, Jia, Zhang, & Wang, 2015).

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References
Ahmed, J., & Salam, Z. (2015). An improved perturb and observe (P&O) maximum
power point tracking (MPPT) algorithm for higher efficiency. Applied
Energy, 150, 97-108.
Saunders, L. J., Russell, R. A., & Crabb, D. P. (2015). Measurement precision in a series of
visual fields acquired by the standard and fast versions of the Swedish
interactive thresholding algorithm: analysis of large-scale data from clinics. JAMA
Ophthalmology, 133(1), 74-80.
Tsoukalas, V. D., & Fragiadakis, N. G. (2016). Prediction of occupational risk in the
shipbuilding industry using multivariable linear regression and genetic
algorithm analysis. Safety Science, 83, 12-22.
Yu, W., Li, B., Jia, H., Zhang, M., & Wang, D. (2015). Application of multi-objective genetic
algorithm to optimize energy efficiency and thermal comfort in building
design. Energy and Buildings, 88, 135-143.