Conflict Propagation and Component Recursion for Canonical Labeling

  title={Conflict Propagation and Component Recursion for Canonical Labeling},
  author={Tommi A. Junttila and Petteri Kaski},
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. 

Conflict Analysis and Branching Heuristics in the Search for Graph Automorphisms

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

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.

Practical graph isomorphism, II

Conflict Anticipation in the Search for Graph Automorphisms

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

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

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

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

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.

A Message-Passing Algorithm for Graph Isomorphism

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


Methods for representing equivalence problems of various combinatorial objects as graphs or binary matrices are considered and can be used for isomorphism testing in classification or generation algorithms.



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

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

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

  • M. Goldberg
  • Mathematics, Computer Science
    Discret. Appl. Math.
  • 1983

Canonical labeling of graphs

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

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

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.

nauty User ’ s Guide ( Version 2 . 4 )

0. How to use this Guide.

Practical graph isomorphism

  • Congressus Numerantium 30, 45–87
  • 1981