Graph isomorphism problem-advance in complexity research

In summary: Your Name]In summary, the conversation highlighted a recent article in Quanta magazine discussing the advancements in complexity research, particularly in graph isomorphism. The article was classified as "intermediate" and was praised for being easy to understand and enjoyable to read despite addressing a challenging problem. The lack of a specific section for graph theory and complexity research in the forum was also noted, prompting a suggestion for its creation.
  • #1
marcus
Science Advisor
Gold Member
Dearly Missed
24,775
792
There seems to have been a major step forward in complexity research. somebody wrote a pleasant understandable piece about it in Quanta magazine.
https://www.quantamagazine.org/20151214-graph-isomorphism-algorithm/

I gave the title an "intermediate" tag because the graph isomorphism problem is simple to state and easy to understand at Undergrad (even high school) level. And the new algorithm that gets a grip on it (without completely solving it) is also easy to describe in elementary terms.

So this makes for a surprisingly easy-to-read enjoyable article, even though the problem is one of the big non-trivial ones in the complexity of algorithms study area.

I didn't see a section of Math forum that is explicitly for graph theory---Topology seemed the closest. Also Topology forum has some threads about combinatorial questions. Nor did i see a section explicitly for complexity research. Like for papers bearing on the "P versus NP-complete" question. Or does this thread belong in the Computation section? If so feel free to move it.
 
Last edited:
Physics news on Phys.org
  • #2


Dear fellow scientist,

Thank you for sharing the article from Quanta magazine about the advancements in complexity research, specifically in the area of graph isomorphism. I agree that this is a major step forward and it is exciting to see progress being made in such a challenging problem.

I appreciate your classification of the article as "intermediate" and I agree that the graph isomorphism problem is simple to state and understand at the undergraduate level. It is encouraging to see that the new algorithm is also easy to describe in elementary terms, making it accessible to a wider audience.

I also noticed the lack of a specific section for graph theory and complexity research in the forum. Perhaps it would be beneficial to create a new section dedicated to these topics, as they are important and relevant in the field of mathematics and computer science.

Thank you again for sharing this article and I look forward to discussing and learning more about the advancements in complexity research with you.
 

1. What is the graph isomorphism problem?

The graph isomorphism problem is a computational problem in graph theory that asks whether two given graphs are isomorphic, or if they have the same structure. In other words, can the vertices of one graph be relabeled in a way that preserves the edge connections and results in the other graph?

2. Why is the graph isomorphism problem important?

The graph isomorphism problem has significant applications in various fields such as chemistry, computer science, and social network analysis. It helps in identifying patterns and similarities between different networks and can aid in solving complex problems in these fields.

3. What are the current advancements in complexity research for the graph isomorphism problem?

Recent advancements in complexity research have shown that the graph isomorphism problem is likely not solvable in polynomial time, meaning it is a difficult problem to solve with current algorithms. However, new techniques, such as theoretical machine learning and algebraic techniques, have shown some promise in solving the problem more efficiently.

4. What is the relationship between the graph isomorphism problem and other computational problems?

The graph isomorphism problem is closely related to other computational problems, such as the subgraph isomorphism problem, which asks whether a given graph is a subgraph of another graph. Other related problems include the maximum common subgraph problem and the graph isomorphism colorability problem.

5. Are there any real-world applications of the graph isomorphism problem?

Yes, the graph isomorphism problem has various real-world applications, such as in the study of molecular structures in chemistry and in the analysis of social networks. It also has applications in computer science, such as in the design of efficient algorithms for solving other computational problems.

Similar threads

Landmark Algorithm for Graph Isomorphism
    • Programming and Computer Science
Replies
3
Views
1K
A Half-face traversal on general polyhedra
    • Topology and Analysis
Replies
9
Views
2K
I Real ODE yields real solution through complex numbers
    • Differential Equations
Replies
3
Views
2K
B Direct and inverse problems
    • General Math
Replies
13
Views
1K
Help to write a psudoecode (formal) of this procedure.
    • Programming and Computer Science
Replies
1
Views
902
A Shinichi Mochizuki's ABC Conjecture and Replication Crisis in Maths
    • General Math
Replies
33
Views
5K
Where Can I Find Resources to Learn Discrete Math for Computer Science?
    • STEM Academic Advising
Replies
1
Views
918
I Understanding Fourier Transforms
    • Other Physics Topics
Replies
1
Views
1K
Other Undergraduate 3rd Year - Need some Academic / Career Advice
    • STEM Career Guidance
Replies
13
Views
2K
Qubits, 2 complex numbers, forcing one to real
    • Quantum Physics
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top