# Fast Algorithm for Graph Isomorphism Testing

@inproceedings{LpezPresa2009FastAF, title={Fast Algorithm for Graph Isomorphism Testing}, author={Jos{\'e} Luis L{\'o}pez-Presa and Antonio Fern{\'a}ndez}, booktitle={SEA}, year={2009} }

In this paper we present a novel approach to the graph isomorphism problem. We combine a direct approach, that tries to find a mapping between the two input graphs using backtracking, with a (possibly partial) automorphism precomputing that allows to prune the search tree. We propose an algorithm, conauto , that has a space complexity of O (n 2 logn ) bits. It runs in time O (n 5) with high probability if either one of the input graphs is a G (n ,p ) random graph, for p *** [*** (ln 4 n / n ln…

## 23 Citations

### Fast Isomorphism Testing of Graphs with Regularly-Connected Components

- Mathematics, Computer ScienceArXiv
- 2011

An algorithm is presented, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are, and preserves all the nice features of conauto, but drastically improves the testing of graphs with regularly connected components.

### Isomorphism Testing via Polynomial-Time Graph Extensions

- Computer ScienceJ. Math. Model. Algorithms
- 2011

A polynomial graph extension procedure that provides a graph coloring capable of rapidly guiding a simple-but-effective heuristic toward the solution of graph isomorphism (GI) properties is introduced.

### Conauto-2.0: Fast Isomorphism Testing and Automorphism Group Computation

- Computer Science, MathematicsArXiv
- 2011

It is proved that, under some circumstances, it is not only possible to prune the search space, but also to infer new generators without the need of explicitly finding an automorphism of the graph.

### A consistency rule for graph isomorphism problem

- Computer ScienceSAC '12
- 2012

The proposed consistency rule is able to prune as early as possible unfruitful branches of the tree-search which leads to reduce the practical time complexity.

### OPTIMIZED BACKTRACKING FOR SUBGRAPH ISOMORPHISM

- Mathematics, Computer Science
- 2012

Two new algorithms for subgraph isomorphism problem for labeled graphs based on modified adjacency list that are competitive with classic Ullman’s algorithm and more recent VF2 are presented.

### Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph

- Computer ScienceJ. Appl. Math.
- 2014

It is formally prove that a GA algorithm that uses these techniques correctly computes the automorphism group of an input graph, as conauto-2.03, which is incorporated into the GA algorithm conauto, with at most an additive polynomial increase in its asymptotic time complexity.

### A polynomial‐time algorithm for simple undirected graph isomorphism

- MathematicsConcurr. Comput. Pract. Exp.
- 2021

This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirectioned graphs are isomorphic or not and proposes the permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not.

### Vsep-New Heuristic and Exact Algorithms for Graph Automorphism Group Computation

- Computer Science
- 2010

One exact and two heuristic algorithms for determining the generators, orbits and order of the graph automorphism group are presented and it is shown that the worst-cases running time of the exact algorithm is exponential but it is polynomial for the heuristic algorithm.

### Isomorphism Test for Digraphs with Weighted Edges

- Computer Science, MathematicsSEA
- 2018

This paper presents a method for extending the applicability of refinement algorithms to directed graphs with weighted edges using {Traces} as a reference software, and substantiates the claim that the performances of the original algorithm remain substantially unchanged.

### Linear Programming Heuristics for the Graph Isomorphism Problem

- MathematicsArXiv
- 2016

An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic,…

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