Landmark Algorithm for Graph Isomorphism

In summary, Quanta Magazine recently published an article discussing a potentially new algorithm for graph isomorphism by Prof Laszlo Babai of the University of Chicago. The article references an Arxiv preprint and explores the implications of this algorithm, which could potentially lead to solutions for other problems previously thought to be unsolvable. The article also mentions the Hungarian roots of many great graph theorists and mathematicians.
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  • #2
A fascinating article jedishrfu. Thanks for sharing that.
 
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  • #3
Super exciting. I always sensed the graph isomorpism problem has never belonged with the others, but when you sit down and try to come up with with an algorithm to prove it, (as I have) it's elusive. I hope this pans out, because pinning down exactly what makes it different could reveal a bunch of other problems that also have solutions in the "metropolitan area of P" previously thought not to.
 
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  • #4
No surprise it was a Hungarian, a lot of great Graph Theorists and Combinatorialists (and general Mathematicians) from Hungary.
 

Related to Landmark Algorithm for Graph Isomorphism

1. What is the Landmark Algorithm for Graph Isomorphism?

The Landmark Algorithm for Graph Isomorphism is a graph matching algorithm used to determine if two graphs are isomorphic, meaning that they have the same structure but may have different labels for their vertices.

2. How does the Landmark Algorithm work?

The Landmark Algorithm works by selecting a set of "landmark" vertices in each graph and comparing the distances between these landmarks in the two graphs. If the distances are the same, then the two graphs are isomorphic.

3. What is the advantage of using the Landmark Algorithm?

The Landmark Algorithm is advantageous because it is faster than other graph matching algorithms, especially for larger graphs. It also has a lower memory requirement, making it more efficient for certain applications.

4. Are there any limitations to the Landmark Algorithm?

Yes, the Landmark Algorithm may produce false positives, meaning it may determine two non-isomorphic graphs as isomorphic. This is because the algorithm only looks at a subset of vertices and does not consider the entire structure of the graphs.

5. How is the Landmark Algorithm used in real-world applications?

The Landmark Algorithm is commonly used in bioinformatics, where it is used to compare biological graphs such as protein structures. It is also used in social network analysis and image recognition to match similar structures.

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