# Recent Advances on the Graph Isomorphism Problem

@article{Grohe2020RecentAO,
title={Recent Advances on the Graph Isomorphism Problem},
author={Martin Grohe and Daniel Neuen},
journal={ArXiv},
year={2020},
volume={abs/2011.01366}
}
• Published 2 November 2020
• Mathematics
• ArXiv
We give an overview of recent advances on the graph isomorphism problem. Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism algorithms with a quasi-polynomial parameterized running time of the from $n^{\polylog k}$, where $k$ is a graph parameter such as the maximum degree. A second focus will be the combinatorial Weisfeiler-Leman algorithm.
12 Citations

## Figures from this paper

We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that
• Mathematics
Graphs and Combinatorics
• 2021
It is proved that some families of Deza circulant graphs have WL-rank 5 or 6 and WL -dimension at most 3.
. It is conﬁrmed in this work that the graph isomorphism can be tested in polynomial time, which resolves a longstanding problem in the theory of computation. The contributions are in three phases as
• Computer Science
Commun. ACM
• 2022
The last few years has been a productive period for research in the field of computational complexity in India, and some of the exciting results include constant factor approximation algorithm for finding a maximum independent set of rectangles, improved bounds for perfect sampling of k-coloring in graphs, an optimal FPT-approximation scheme for k-way cut, and a new online algorithm for caching.
• Computer Science
2022 4th International Conference on Process Mining (ICPM)
• 2022
The case concept for object-centric process mining is introduced: process executions, which are graph-based generalizations of cases as considered in traditional process mining and determine equivalent process behavior with respect to an attribute using graph isomorphism.
• Mathematics
STOC
• 2022
We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph H as a minor can be solved by an algorithm working in time f(H)· nO(1), where f is some function. In other words, we
• Mathematics
Journal of Algebraic Combinatorics
• 2022
An (association) scheme is said to be Frobenius if it is the scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be
• Education, Computer Science
ArXiv
• 2021
A comprehensive overview of the Weisfeiler–Leman algorithm’s use in a machine-learning setting, focusing on the supervised regime, and discusses the theoretical background, how to use it for supervised graph and node representation learning, and recent extensions.
• Computer Science
NeurIPS
• 2021
This work shows the extent to which graph reconstruction—reconstructing a graph from its subgraphs—can mitigate the theoretical and practical problems currently faced by GRL architectures and demonstrates how it boosts state-of-the-art GNN’s performance across nine real-world benchmark datasets.

## References

SHOWING 1-10 OF 96 REFERENCES

We relate the graph isomorphism problem to the solvability of certain systems of linear equations and linear inequalities. The number of these equations and inequalities is related to the complexity
In this paper we construct a polynomial algorithm for verifying the isomorphism of graphs which do not pinch to K3,g. In the construction we use properties of colored graphs from this class and
• Mathematics
2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
• 2018
This work gives an improved isomorphism test for graphs of small degree: their algorithms runs in time n^O((log d)^c), where n is the number of vertices of the input graphs, d is the maximum degree of theinput graphs, and c is an absolute constant.
• Mathematics
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
• 2020
We prove that there is a graph isomorphism test running in time $n^{\text{polylog}(h)}$ on $n$-vertex graphs excluding some h-vertex graph as a minor. Previously known bounds were
• Mathematics, Computer Science
ICALP
• 2015
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Grobner basis computation. The idea of these algorithms is to encode two graphs into a system of
• Computer Science
J. Symb. Comput.
• 2014
The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned.
It is shown that for every surface S, there is a k _> 1 such that the k-dimensional WL-algori thm succeeds to decide isomorphism of graphs embeddable in S.