THE AUTOMATED FLOWCHART DESIGN AND CODE WRITING SYSTEM

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SOME OTHER INTERESTED SORT ALGORITHMS

It is my personal opinion and experience that a key to innovate or discover new algorithms is to first understand the operation of existing algorithms. Understanding the way an algorithm operates is more important than doing a mathematical analysis of its complexity. This seems to be the tendency of some authors in the literature and they find it difficult to accept any idea that is new or different. The most they seem to be able to do is present useless abstract mathematical analysis followed by speculative statements about what their mathematical conclusion might be saying. Understanding the way an algorithm actually work takes more than a mathematical analysis does. Mathematics can be a dumb tool for some who does not have the capacity for spatial or temporal manipulation of a concept or a process so as to understand its actuality or generality!

Following these presentation, I show you an optimum merge-sort algorithm that does sort in-place with O(N) data move operations. This algorithm is an application of the concept of the Internal buffer and Block rearrangement to k-way merge-sort. I have also managed to, by perseverance and in spite of characters with the unfavourable attributes mentioned above innovate an algorithm that uses no more than N\lceil log₂N\rceil - \lceil log₂N\rceil +1 comparisons and 2N data moves. We implement similar algorithm to do stable sort using the same number of comparisons and no more than N data moves. We map this technique onto a mesh to get a log₂N debt sort network.

OTHER NEW MERGE AND SORT ALGORITHMS

As a note of caution. Most if not all of these algorithms were submitted to Academic Journals but were rejected for reasons such as Lack of Understandability on the part of the reviewer, Misunderstanding of the function or nature of the algorithm, Inappropriate submission, among other unreasonable or odd reasons. Some areas of discussion in these papers are technically very difficult to read and some claims are difficult to verify. They require expertise in this area of algorithm analysis and they are not base on Mathematical theorems or axioms. These algorithms are techniques for the systematic spatial manipulation of sequenced data in order to achieve a given permutation. They are not mathematical or theoretical explanation of physical phenomena!

The area of sorting data on uniprocessor digital computer systems is well researched. My previous research supervisor feels that there is not much left to be discovered in this area. But I was convinced that there is/was a problem that need to be solved before we can continue to look at multiprocessor systems or solutions. I have also discovered from my experience that some academic experts are not as expert as they would like others to believe. However, if you are open minded, without much academic pride or frustration in this area and have the equivalent experience of at least "A" level mathematics, then it is more likely that you will read and understand the basic ideas of these discussion papers. This I say from my personal experience as a tutor and as a supervised researcher. If you do not have a lot of knowledge in this area, you do not necessarily have to worry. You may have a kind of virtue that puts you way ahead of others that rely a lot on vices. "Wisdom is like an eternal engine constructed from all kinds of virtues but the eternal doom of a fool are the devices that he relies on!" "It is better to be wise than to be clever! The former confirms and consolidate your virtues but the later will only make you more conceited."

Even Merge

An O(n²) unstable in-place merge-sort algorithm on a uni-processor computer system with AT² complexity of O(n\sqrt(n)) on a mesh-connected MIMD multiprocessor system. Abstract given below. The expression ( AT²) area-time squared complexity is a theoretical way of looking at the usefulness of an algorithm in terms of the amount of space (area) that would be needed to implement it on a two-dimensional (2-D) surface and its time performance. I'll tell you more about this later on.

Actually, an algorithm is usually not implemented on a surface! A distinguishing feature of algorithms is that they are temporal in nature. I.e. the objects they work on or affect changes over time in an orderly manner. However, the sequence of events that an algorithm must pass through in order to achieve its object are some times very weakly coupled or not coupled at all in this respect. Hence, it is possible to identify specific activities for events within the algorithm sequence where the activity can be done out of sequence with little or no regard for some other or no other activities. Hence, it is possible in some algorithms to identify activities that can be done in parallel with pre-sequenced activities or ahead of these activities. The actual way to determine these parallelisms can be complex but I am not too certain that there is much research work done on this in the literature.

The product of the spatial Two-dimensional values and operational Time squared is a limiting factor on performance when these systems are implemented on 2-D surfaces. Hence, theoretically there is an optimum performance that one can not exceed when implementing a permutation algorithm on a 2-D surface. Similar and related to the the theoretical limit on the lowest number of comparisons you can do when implementing a comparison base sort algorithm. I would think that all surfaces are 2-D! Just for fun, I would think that there is also a VT³ complexity for 3-D volume! I should probably look at this more seriously later on!

You see multidimensional (multiprocessor) sort algorithms are often looked at in terms of their physical implementation along with their time performance. Uni-processor sort algorithms are also analysed in terms of their physical implementation but this is in terms of a simple RAM model. I have already mentioned some of the terms used to describe attributes of these algorithms.

Shuffle Merge

An O(nlg²(n)) unstable in-place merge-sort algorithm on a uni-processor system with high degree of parallelisation in its implementation. Actually, the algorithm merge by a process of iterative un-shuffling of a permutation. Unfortunately, some frustrated readers have misunderstood the operation of the algorithm to be that of odd-even transposition sort.

Shift Merge

An in-place merge algorithm that merges two pre sorted lists by block rearrangement without the need for an internal buffer. The algorithm needs to be properly analyse in order to determine its asymptotic operational time complexity.

I am preparing all these document so that they can be printed as a single book but I will not put my main network sorting ideas in this book until I have applied for a patent. I have been given enough wisdom to come to the realization as to how the system of commercial patent work in tandem with academia. This is a corrupt evil system base on deception and theft! I will make it available over the Internet.

Please be warned! Some of the reading is very involved and difficult to follow (read). In some instance you may have to be an expert in this area of research to follow or know what to look for or ignore but do not ignore godly wisdom.