Volume 1: Student Life Chapter 322: What is the revelation of NP-complete problems?
Seeing this, Chen Zhou smiled and shook his head.
He felt that Zhao Qiqi and Zhu Mingli had completely reached the state of letting themselves go.
As for Li Li, he did not let himself go.
Firstly, he has a rather introverted personality, and secondly, he simply doesn't have the conditions to let himself go!
Ever since he got together with Li Jing, he has been controlled by Li Jing...
Turning his attention back to the computer web page, Chen Zhou's hand that was sliding the mouse wheel suddenly paused.
It was not because of the content in front of him, but because he suddenly remembered that the avatar he saw on Zhu Mingli’s mobile phone just now, why did it look so familiar?
"Professor Zhang again?"
Chen Zhou couldn't help but feel a little amused. He still remembered what happened on the campus Internet.
But I didn't expect that Professor Zhang Zhongyuan actually likes to hang out on the campus network so much.
Is it only by getting along well with students that I can prove that I have always been young?
Not necessarily? At least the head doesn't look like that...
"Design a pentagon that can fill a plane without leaving any gaps. How many pentagons are there?"
This is the problem of "plane tessellation", and it is also a difficult problem that has always plagued the mathematical community.
There are many applications of tessellation theory, such as how to maximize space utilization and save costs when stacking objects.
In crystallography, how to optimize the crystal structure also falls within the application scope of tessellation theory.
However, because each interior angle of a regular pentagon is 108 degrees, which is not a factor of 360 degrees, it is impossible to tile the plane densely, and the only way to challenge this problem is to use deformed pentagons.
One of the 11 major events in mathematics is that mathematicians have finally found the 15th pentagon.
This is also one of the two things that Chen Zhou is interested in.
Chen Zhou looked at the 15 patterns covered with pentagons on the web page with great interest.
The pentagon problem is an area of geometry that interests most mathematicians because it is the only shape that is not yet fully understood.
This 15th pentagon is also the first pentagon that meets the requirements discovered in 30 years.
Chen Zhou thought for a moment, then slid the mouse to look at the next event of interest.
Now, he is simply interested and has no intention of investing in the field of geometry immediately.
Another thing that Chen Zhou is interested in is the progress of the graph isomorphism problem.
This has been a special problem in complexity theory.
Simply put, it is a question of whether a regular pentagon or a five-pointed star is isomorphic, that is, whether there is a one-to-one correspondence between points.
The description of this incident is about a paper presented by Professor Babai of the University of Chicago at a seminar in 2014.
His work aimed to show that the problem could be solved in quasi-polynomial time, which is slightly longer than polynomial time.
His results were also recognized by most mathematicians, who believed that this would be a great breakthrough in this field.
It will also shed light on the million-dollar "P/NP problem".
That’s right, it’s the “P/NP problem”, one of the seven Millennium Problems.
The same as the famous "Hilbert's 23 Questions" proposed by Hilbert at the International Congress of Mathematicians in 1900.
These are seven world-class mathematical problems announced by the Clay Mathematics Institute in the United States on May 24, 2000.
The prize for each puzzle is $1 million!
The seven Millennium Problems are NP-complete problems (P/NP problems), Hodge conjecture, Poincare conjecture, Riemann hypothesis, Yang-Mills gauge field existence and mass gap hypothesis (gauge field theory), existence and smoothness of solutions to the NS equations, and BSD conjecture (Bech and Swinnerton-Dyer conjecture).
So far, only the Poincare conjecture has been solved by Russian mathematician Perelman.
“Does it have implications for NP-complete problems?”
Comparatively speaking, among these 11 major events, this one is the one that Chen Zhou is most interested in.
After all, it is a study related to the Millennium Problem.
Although for many people, the last of the 11 major events, that is, the Chen Zhou incident, may be more eye-catching.
Regarding NP-complete problems, let’s take a simple example.
One night, you went to a party. Because the party was so grand, you felt uneasy and wanted to know if there was anyone you knew in the whole banquet hall.
Just at this moment, the host of the party suggests to you that you must know the lady who is eating ice cream near the dessert plate.
It takes almost no time for you to glance over there and see that the host of the party is correct.
However, if there is no such hint, you must look around the banquet room, examining everyone one by one, to see if there is anyone you know.
It's actually like if someone tells you that 13717421 can be written as the product of two smaller numbers.
You will definitely hesitate and wonder if what he said is right.
However, if he tells you that 12717421 can be decomposed into 3607 times 3803, you will quickly get the answer and verify that it is correct.
This is a simple example of an NP-complete problem.
As for the NP-complete conjecture, it means that all completely polynomial non-deterministic problems can be converted into a type of logical operation problems called satisfiability problems.
All possible answers to this type of question can be calculated in polynomial time. So is there a deterministic algorithm for this type of question that can directly calculate or search for the correct answer in polynomial time?
It sounds simple, but verifying it is a completely different matter.
NP-complete problems are also one of the most prominent problems in logic and computer science.
Even though computer science is developing rapidly, the answer to this question remains unsolved.
Gently shaking his head, Chen Zhou threw away the messy thoughts in his mind. Regardless of whether it could really provide inspiration for NP-complete problems, he had to take a look at Professor Babai's paper.
It just so happens that he also started learning computer science today.
After returning the computer to Li Li, Chen Zhou discovered that Zhu Mingli had not come back yet. He couldn't help but feel amused. What kind of secret could this be that would make him run away rather than keep it secret?
"Brother Chen, um, can I ask you a question?" Li Li took the computer and said hesitantly.
Chen Zhou glanced at Li Li, then patted him on the shoulder and said with a smile: "Just say whatever you want to say, kid. Why are you hesitating?"
Zhao Qiqi also came up and said, "That's right, Brother Chen is not a stranger. What's the matter, two LIs, are you still unfamiliar with them?"
Li Li smiled shyly: "No, no..."
Chen Zhou looked at Li Li, wanting to say something, but in the end he didn't, and just asked, "What's the problem?"
Li Li took out his notebook, turned to the content he had just written today, and pointed to the formula : "It's about the distribution deconstruction method. I studied this part for a long time, but I still don't understand it."
Chen Zhou took a look and a smile appeared on his face.
