# Conflict Propagation and Component Recursion for Canonical Labeling

@inproceedings{Junttila2011ConflictPA, title={Conflict Propagation and Component Recursion for Canonical Labeling}, author={Tommi A. Junttila and Petteri Kaski}, booktitle={Theory and Practice of Algorithms in (Computer) Systems}, year={2011} }

The individualize and refine approach for computing automorphism groups and canonical forms of graphs is studied. Two new search space pruning techniques, conflict propagation based on recorded failure information and recursion over nonuniformly joined components, are presented. Experimental results show that the techniques can result in substantial decrease in both search space sizes and run times.

## 45 Citations

### Conflict Analysis and Branching Heuristics in the Search for Graph Automorphisms

- Computer Science2013 IEEE 25th International Conference on Tools with Artificial Intelligence
- 2013

To support backjumping, high-performance search for graph automorphisms is extended with a novel framework for conflict analysis, and techniques from the constraint programming and satisfiability literatures are adapted.

### 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.

### Conflict Anticipation in the Search for Graph Automorphisms

- Computer ScienceLPAR
- 2012

Prior algorithms for the graph automorphism problem are improved by introducing simultaneous refinement of multiple partitions, which enables the anticipation of future conflicts in search and leads to significant pruning, reducing overall runtimes.

### Novel Techniques for Automorphism Group Computation

- Computer ScienceSEA
- 2013

This work proposes four novel techniques to speed up algorithms that solve the GA problem by exploring a search tree by allowing to reduce the depth of the search tree, and by effectively pruning it.

### Canonical Forms for General Graphs Using Rooted Trees - Correctness and Complexity Study of the SCOTT Algorithm

- Computer Science
- 2020

These proofs ensure that the three canonical forms provided by SCOTT are valid, namely a canonical adjacency matrix, a canonical rooted tree (or DAG) and a canonical string.

### A Polynomial Time Algorithm for Graph Isomorphism and Automorphism

- Mathematics, Computer Science
- 2021

It is proved that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees, and introduced a new tree data structure called Walk Length Tree.

### Recent Advances on the Graph Isomorphism Problem

- MathematicsArXiv
- 2020

The main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphicism 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.

### Representing Equivalence Problems for Combinatorial Objects

- Computer Science, MathematicsSerdica Journal of Computing
- 2015

Methods for representing equivalence problems of various combinatorial objectsas graphs or binary matrices are considered. Such representations can be used for isomorphism testing in classification…

### A Message-Passing Algorithm for Graph Isomorphism

- Computer ScienceArXiv
- 2017

A message-passing procedure for solving the graph isomorphism problem is proposed. The procedure resembles the belief-propagation algorithm in the context of graphical models inference and LDPC…

## References

SHOWING 1-8 OF 8 REFERENCES

### Search Space Contraction in Canonical Labeling of Graphs (Preliminary Version)

- Computer ScienceArXiv
- 2008

The individualization-refinement paradigm for computing a canonical labeling and/or the automorphism group of a graph is investigated and a new partition refinement algorithm is proposed, together with graph invariants having a global nature.

### Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs

- Computer ScienceALENEX
- 2007

Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed.

### A nonfactorial algorithm for testing isomorphism of two graphs

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 1983

### Canonical labeling of graphs

- MathematicsSTOC
- 1983

An algebraic approach to the problem of assigning canonical forms to graphs by computing canonical forms and the associated canonical labelings in polynomial time is announced.

### Isomorhism of Hypergraphs of Low Rank in Moderately Exponential Time

- Mathematics2008 49th Annual IEEE Symposium on Foundations of Computer Science
- 2008

The case of bounded k answers a 24-year-old question and removes an obstacle to improving the worst case-bound for Graph Isomorphism testing.

### Faster symmetry discovery using sparsity of symmetries

- Computer Science2008 45th ACM/IEEE Design Automation Conference
- 2008

A new symmetry-discovery algorithm which exploits the sparsity present not only in the input but also the output, i.e., the symmetries themselves, which improves state-of- the-art runtimes from several days to less than a second.

### Practical graph isomorphism

- Congressus Numerantium 30, 45–87
- 1981