The definitions at the top of some pages above the horizontal bar are probably well intentioned, but: (1) just remove "|G| is the vertex cardinality (number vertices) of graph G", the reader must be able to guess this sort of detail, if he is qualified enough to understand such a text. (2) don't remove "In a search tree, a Discrete Partition or Individualization-Reļ¬nementPath is a path which starts at the root and ends in a leaf [1].", but try to include it in the normal text.
I won't have time before next Tuesday to give you significantly more feedback...
@ThomasKlimpel No problem, Thanks for your time. BTW: "if he is qualified enough to understand such a text.".....You would be surprised to know it is not true, you know how complicated writer I am , yet I have included that kind of "silly" thing! why? cause I found objection. Good Night!
" but try to include it in the normal text.".... the final draft will be more nicely arranged.
FYI: I am considering an undergraduate online Journal . So,....
@ThomasKlimpel , If you finish reading 0.2, read researchgate.net/publication/… , read section 3,4,5 for the final result. Do you think , the result is above threshold of undergrad journal?
If you want to publish something, you should at least have a key message and a target audience. And you should be aware that even if you don't have a key message, your writing will send some key messages to its readers. For the current condition of your draft, I got the following messages: (1) You have some ideas, which are more or less clear in your mind. (2) You are willing to put in quite some effort to communicate those ideas to people who are willing to communicate with you.
@Jim What is your key message? Who is your target audience? Do you expect undergraduate journals to be the places where undergraduates can submit papers which nobody is expected to read?
Seriously, when you wrote your first drafts before Babai's breakthrough, I could see key messages like (a) shooting for a reachable goal (quasi-polynomial) instead of a goal with known barriers (poly time algo for GraphIso, while no poly time algo for GroupIso is known yet), (b) using a more or less natural approach and tackling the difficulties one at a time.
Why do you write stuff like "... then $O(\beta^x) = O(1)^x$, so graph isomorphism can be determined in $O(n) + O(\beta^x) = O(n) + O(1)^x=O(n)$ steps."? Is this supposed to be funny? Let me apply this logic to a simpler case: $O(2^n)=O(2)^n=O(1)^n=O(1^n)=O(1)$. Cool, so my brute force search for SAT actually runs in constant time. Really?
@ThomasKlimpel If $y_k = log(n)$ then I can do linear time (Babai Can't do that) + the performance depends on the $y_k$, as $y_k$ increases, the algo becomes better+ IMHO , it is a good approach for practical use. "Do you expect undergraduate journals to be the places where undergraduates can submit papers which nobody is expected to read?" - certainly the quality threshold is not same, like professional journal, is not it?
@ThomasKlimpel also the approach is novel (completely different framwork), and has future prospect. I am sure, even in the professional journals, every result is not the best one.
you think the idea has not passed the threshold for Undergrad journal yet ?
@Jim I don't know the details of the journal you are targeting. I hadn't heard of undergraduate journals before. But even an undergraduate journal should have a target audience...
I am not familiar with the concept "target audience" , especially, it is hard to understand in undegrd journal context as I am an unergrad with no publication.
@Jim I will review them after next Tuesday, maybe I will change my mind then. By "target audience", I ask who you want to reach, who is the person you hope will read your article. And the "key message" is want you want that person to learn from reading your article.
fine, but even if x is a variable , is it a bad result?
why I have to give the break through ?
you have not commented on "even in the professional journals, every result is not the best one."
My motivation behind publishing it is to establish a Framework, on which I will move on.
If the idea is correct and reviewed (the job of journal), it makes it more convenient to work with, I should not handle the pressure that I might have made a mistake in the beginning .
=D =D it appears to me that you expected me to give the Quasipolynimial algo before Babai, since I could not do that , there is no point working/publishing on GI for me!
@ThomasKlimpel Sorry for the confusion, but I hope I am have explained what I meant by that.
@Jim No, you don't need to give the break through. I just asked you about your "target audience", and your "key message" for that audience. If I should help you write improve your writing, it is also part of the writing process to know that you write for somebody, and that you want to tell your reader something.
I know that it might be a difficult question, but why not try to answer it?
@ThomasKlimpel Sir, the problem is I don't understand the question completely as i am not familiar with these 2 concept. to me, If anything is good (faster or good upper bound), or novel + has some promise or if it is good for some case then it is worth publishing. The definition of "good" result depends on the quality of journal. but every peer reviewed paper is correct, may be all of them might not be good or important.
let me answer your way: key message : 1. I solve GI for a restricted class better than babai (My claim! :) ) 2. The idea is practicable for a large class though it might not be faster than the established theoretical result which are extremely hard to implement. (I am sure you are aware that Practical and theo: aspect of GI is different). 3. The idea shows a prospect.
Target Audience : Any time, audience is academic (who else would read this!!), it is trivial. The question should be regarding the quality of academic (similar situation like "good journal" ). At the moment I don't care who read it. I just want it verified, at the moment, so I can work on an established ground. For example, if I get published in a peer reviewed journal, It is lot easy to discuss with an academic since the result is verified= peer reviewed.
For example, now I am explaining you the whole Idea , but if it was published, I would not need to explain this to you since it is a published work , then we could start where the paper ended, for example my current draft shows $\beta^x$, if it was published, then we would start our talk on how it can be made constant.
Room for Jim and Thomas Klimpel
Room for Jim and Thomas Klimpel