I studied this algorithm for a lot of years and I am very sure it is correct. It does not need you too much time to understand it, because I show how to understand it in the abstract and remarks. This is my paper’s website:

https://arxiv.org/ftp/arxiv/papers/1004/1004.3702.pdf

But now I meet some problems that need your help and cooperate. As a coauthor, you can discuss with me and I can explain every possible doubt of you.

1) A top journal said my English expression is hard to follow, and suggested me to find a person to cooperate who is strong in algorithm and also strong in English paper writing.

2) A top journal said NP cannot equal P, next are their comment and my answer:

Their rejecting email:

Although it remains a logical possibility that the P=NP? question has a positive answer, the overwhelming view of the research community is that its liklihood is negligible.

The sincerity and technical ability reflected in your submission led us to an initial effort to recruit a reviewer who might be willing to try identifying your work. We regret that we could not find such a reviewer. No competent reviewer we know of willing to put in the effort to find a bug in a sophisticated densely written 40 page paper.

My answer:

At present, most of well-known authorities in this area tend to think that NP is not equal to P. It is absolutely certain that the authorities have no strong basis for this view, but this view seems to have been tacitly accepted by most people.

As a result, various academic papers often talk about NP, especially NPC, directly declare that there can be no polynomial time algorithm. Such acquiescence is undoubtedly harmful.

A top international journal should be a responsible journal. To reject an algorithm paper, they should make sure that the algorithm is not innovative or is wrong. My paper is only an algorithm, the right or wrong of the algorithm is not difficult to determine. I can explain any doubts. In order to understand my algorithm, one only needs to understand series of destroying edges. I said it again: one only needs to understand series of destroying edges. This is a very possible job. Why don't you read it carefully and then understand it? However, some top journals often reject papers based on guesses and assumptions rather than carefully reading and understanding them. Some journals reject my paper for two reasons: 1) It is impossible for you, an ordinary and unknown person, to solve such a difficult problem, and your paper must be wrong. But how many major problems have been solved in history, and the solvers are not ordinary people before solving them? 2) Experts generally believe that NP is not equal to P, so your paper that NP is equal to P cannot be correct. My answer is: only strictly proven conclusions are meaningful. Why do some experts always like to assert something? How many experts have asserted somethings in history, and later these assertions have been broken by new achievements. Let's briefly discuss why some experts assert that NP is not equal to P.

Two famous scientists on algorithm wrote in one of their books[22] that so far a large number of NP-complete problems have arisen. Because many excellent algorithm scientists and mathematicians have studied these problems for a long time, but have not found a polynomial algorithm, then we tend to think that NP is not equal to P. Such inferences are logically untenable. From another point of view, there are so many NP-complete problems that no algorithm scientists or mathematicians can prove that any problem is exponential.

Lance Fortnow, the editor-in-chief of a famous ACM journal, wrote a review of P. vs. NP [23], in which he believed that: 1) no of us really understood NP, 2) NP was unlikely to equal P (unlikely), and 3) human beings could not solve the problem in a short time (as explained above, this assertion is meaningless). To illustrate that NP is not likely to equal P, he described a very beautiful world under the premise that NP is equal to P: all parallel problems can be solved in polynomial time, all process problems, optimization problems, Internet paths, networking problems, etc., can quickly get the best solution, even all number problems. The solution of hard problems can also be completed quickly in polynomial time, because solving any mathematical problems is actually a parallel, multi-branch, exponential expansion process. There may be only one correct channel for it. This is actually an NP problem. So he thinks that if anyone proves NP = P, it means that he has solved all seven world problems. He did not say that if anyone proves NP = P, then who can control the whole universe, because the evolution of the universe, including human intelligence activities, can theoretically be seen as a multi-branch, continuous parallel development process. The real world we are in at this time is only one of its branches, or just a possibility of its evolution and development. Despite Mr. Lance Fortnow's authority (editor-in-chief of internationally renowned journals), his argument is logically untenable. Even in his own article, he admits that even if NP = P is proved, it does not mean that we can get an efficient polynomial time algorithm for any NP problem. Here I change his view slightly: if human beings have got unlimited Non-deterministic Turing machine, the wonderful world he describes can indeed appear. What does it mean to have an unlimited Non-deterministic Turing machine? It means that you have countless labor forces that work for you on your own terms, without overlapping, along different branches. Imagine that if you had countless mathematicians who were going to tackle a math problem in parallel along all possible directions (branches). What math problem would not be solved quickly? However, NP = P is not equivalent to having unlimited Non-deterministic Turing machines. Logically, it is impossible for human beings to create unlimited Non-deterministic Turing machines.

Hilbert, a great mathematician of the twentieth century, has a famous saying: we must know; we will know. It can be seen that Hilbert essentially agreed that NP equals P. Many mathematical problems in human history, including Hilbert's famous 23 mathematical problems, are constantly being solved. Isn't it a confirmation that NP equals P?

From the heuristic point of view, any NPC problem can be reduced to any other NPC problem in polynomial time. That is to say, every distance between two NPC problems is polynomial. The fact itself strongly shows that NP problems have a unified solution law and difficulty, and its solution difficulty should be polynomial order of magnitude. The difference of an attribute value between any group of individuals in the objective world is usually in the same order of magnitude as the absolute value of an individual attribute. For example, one adult weighs in 100 pounds, and the difference between a very fat man and a very thin man is also in 100 pounds. Similarly, the weight of an ant is in gram, and the difference between a big ant and a small ant is also in gram. Etc. Of course, these are not strictly proven conclusions.

Anyway, I studied this algorithm for many years and I am very sure I am correct. Remember Calois, E? There are a lot of Cauchys and Fouriers in this world, but I believe that I can meet a Joseph Liouville.

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